Ten years ago, it was the official policy of the Mobil Oil Corp. to reject requests for contributions to arts and cultural programs. "That's what corporations did at that time," said Earl Whitcraft, secretary of the Mobil Foundation. "There was no feeling that support of the arts should tie in with our corporate obligations. The arts were viewed as a thing apart from business."

Last year, however, Mobil and the Mobil Foundation gave more than $7 million to arts and cultural programs. Most of that money was funneled to network television specials and public television series such as "Upstairs, Downstairs" and other "Masterpiece Theater" productions," but slightly more than $1 million went to ballet troupes, theater groups, symphony orchestras, operas and other arts activities.

Throughout the American corporate community, the story is much the same. American business, which gave $22 million in support of culture and the arts in 1967, last year donated $221 million - a sum more than double the 1976-77 government allotment to the National Endowment for the Arts.

One company, Exxon, is now said to be the largest single private supporter of the arts in the United States, having displaced such traditional and well-known philanthropic organizations as the Rockefeller and Ford Foundations. Eleven others, says a study recently published by the Business Committee for the Arts, last year donated at least $1 million each to arts and cultural programs. As one executive at the Allstate Insurance Co. puts it, corporate involvement in the arts has now reached the point where "it has as many flavors as Howard Johnson has ice cream."

The reasons for this dramatic increase in corporate support of arts programs are many. Public relations has much to do with it, to be sure: Many companies disburse their arts funds through their public relations, advertising, communications or public affairs departments, and most frankly admit that "image awareness" and "visibility" are factors in arts funding decisions.

The major oil companies, targets of much criticism as a result of the energy crunch and the high profits it has generated for them, have become an especially active force in the corporate arts area. According to a recent study done for the BCA by the New York accounting firm of Touche Ross, five major oil companies that donated a total of just under $2 million dollars to the arts in 1973 - the last year of cheap gasoline and no energy worries for the American public - gave over $12.5 million last year, a 540 per cent increase in four years.

"The most visible ones in the field are the oil companies, and for a couple of reasons," says Donald S. MacNaughton, chairman of the board of the Prudential Insurance Corp. and a member of the board of directors of Exxon and AT&T. "The main one is that they don't have to advertise their gasoline. They're selling more than they want to sell. So there's a vast amount of money that can go into the performing arts.

"Secondly, the industry, rightly, or wrongly, has a bad image, and they're using this as a means of trying to improve it."

There can be substantial tax advantages in such corporate funding of arts programs through advertising budgets and company-funded and company-staffed foundations. The Internal Revenue Code permits corporations to deduct up to 5 per cent of their pre-tax income for charitable deductions, and the arts share of this philanthropic dollar has been rising steadily. The Business Committee on the Arts, the corporate arts support organization founded by David Rockefeller in 1967, estimates that the arts received 11.6 per cent of the business charitable dollar last year, up from 8.7 per cent in 1973.

According to Louis Harris, the poll-taker, the public demands no less. At a meeting of the American Council of the Arts in Atlanta last month, he noted that 55 per cent of the American public believe that "business should support art museums." Almost as many think that business has an obligation to support symphony orchestras, theater groups and opera and dance companies.

The business community itself seems to be coming around to this way of thinking. Many corporate leaders, when questioned about reasons for the tenfold increase in corporate support of the arts over the last decade, toss out such phrases as "community responsibility" and "concern with the quality of life." Others express concern over government involvement in the arts. All, however, agree that the role of business is large - and will increase.

"The arts are in trouble," says Thornton Bradshaw, president of the Atlantic Richfield Co. "If things were going swimmingly well, I don't think you'd see as much movement on the part of corporations."

It's ironic that the trouble is not with audiences. More people than ever want to partake of arts offerings - a rise in popularity that places enormous strains on existing arts programs and organizations, with their limited staffs and budgets and rising costs, and creates a need for new arts groups and more money. The demand is there, but the funding isn't.

"The arts are experiencing a vacuum as far as financial support," says Prudential's MacNaughton. "My feeling is that that vacuum will be filled, because I can't conceive of a nation like ours neglecting the arts. It will be filled by one source or another: either government or some kind or private support.

"There are fewer and fewer of the very large family fortunes and private foundations the arts used to rely on, so where is the money going to come from? Corporate America is where it's got to come from, and that's where it will come from. If it doesn't, then I think there is a great danger the arts will be dominated by government."

Whether corporations are above domination of programs they support remains to be seen. Many artists, for example, are watching carefully for signs that the corporate sugar daddy may turn sour when confronted with the unexpected - as Mobil did this week when it withdrew its $500,000 grant to a Columbia University journalism program partly because, according to Elie Abel, dean of the School of Journalism, the newly named director of the program had written a book critical of the oil industry.

It's clearly these giants of the Fortune 500, not the little mom-and-pop businesses or even medium-sized corporations, that have taken the lead in corporate arts funding. A recent BCA study revealed that almost half of all corporate arts donations came from the 758 companies with total sales of more than $500 million annually - the top 1 per cent of the American corporate community.

There are occasionally dissenters even within that elite group, of course. The unnamed "chairman of a major chemical company" expressed his doubts to The Conference Board, a New York-based business research group, this way: "The central questions relates to the corporation's need to restrict use of stockholders' money to those activities that have a demonstrable relationship to the interests of the business. In areas other than this, contributions are a matter for the individual stockholder."

But this is decidedly a monority view. The BCA estimates that 92 per cent of all American corporations supported at least one arts programs last year. More than two-thirds made donations to symphony orchestras, over half to museums. Public radio and television, arts centers, opera, arts councils and historical and cultural restorations were other favorite areas of support.

The emphasis in nearly all these programs is on activities in communities where the corporation has plants or offices - or on prestigious, high-visibility shows in "national halls" such as the Kennedy Center and Ford's Theater in Washington or Lincoln Center and the Museum of Modern Art in New York. "I guess there probably is a kind of 'wealth attracts wealth' syndrome at work," Thornton Bradshaw admits. "Maybe there shouldn't be, but there is. You can only mount a major exhibit at a major museum."

"Corporations usually don't like to get involved with avant-garde projects," says Odile Jacobs, arts specialist for Philip Morris, which is currently underwriting a Jasper Johns exhibition at the Whitney Museum that was considered and then, according to a source involved in the show, rejected by Exxon. "They like to appeal to as many people as possible, so they avoid anything that's controversial."

So while such proven but safe PBS fare as "The Adams Chronicles" and the BBC imports "Upstairs, Downstairs" and "Civilisation" readily gain corporate underwriting, experimental, innovative programs such as "Visions," a critically acclaimed PBS series of original works by new American playwrights, have a much harder time of it.

"Corporations aren't going to buy a pig in a poke," says Ed Hymoff of the Corporation for Public Broadcasting, which has decided to renew "Visions" out of its won funds. Things like "The Adams Chronicles" and "Masterpiece Theater" are a known entity. They're not something that people could possibly take the wrong way.

"Visions' hasn't got the private industry funding we had hoped for. It was very creative, unstructured, and not at all what they were expecting."

"In evaluating a request for an arts grant," says MacNaughton, "you use the same criteria you would apply to any investment decision. You find out what they want, why they want it, what they've done in the past with the money, have they been responsible, is it a well-managed institution, and so on."

Such decisions usually are made or at least approved by the board of directors of a company or foundation - though the Atlantic Richfield Foundation also seeks advice on the performing arts from Beverly Sills and on visual arts from Herbert Bayer, one of the last surviving members of the Bauhaus group.

"Like all profit-making organizations," says Thomas A. Yates, director of communications for the Wm. Underwood Co., "we are interested in the bottom line. Increasing and improving our cultural surroundings is a worthwhile goal in itself, and it also has its benefits for the company. We support the arts because it's good business."