Burlington Northern Inc., one of the investment community's favorite railroads, has made a long-awaited diversification move by offering about $600 million for a controlling interest in The El Paso Co., California's leading supplier of natural gas.

What's in it for the railroad-dominated firm is a chance to spread its muscle throughout the West on the eve of another aglomeration that will create one of the largest railroads in the country. Just today, Chief Justice Warren Burger refused to hear arguements challenging the Union Pacific Corp.'s acquisition of Missouri Pacific Corp. and Western Pacific Railroad, clearing the way for one of the most significant deals in railroad annals.

"The move for El Paso makes sense for them," noted Andras Petery, a leading rail analyst with Morgan Stanley & Co. Inc. "It is a big, big step and we hope they exercise discipline. It is absolutely crucial to link this event with their railroad prospects.

"The first and foremost mission of this management, and other railroads, for that matter, should be to enhance their prospects and minimize the effects from the big Pacific railroad," Petery said. "The acquisition should not be at the expense of the railroad."

Most Wall Street analysts expect the deal to work, if perhaps at a price higher than the $24 a share Burlington has offered. "I believe Burlington stands a good chance of being successful in their effort, but I also expect El Paso's management to not like their price," said Robert Long of First Boston Corp. "The possibility exists of a higher offer."

Should the El Paso deal work, it would be the first major step in a diversification strategy set by the railroad's chief executive, Richard Bressler.

Bressler goal is to move Burlington away from its more than 85 percent revenue dependence on its 29,000-mile rail business with a target by the end of the decade of a 50-50 split. "Our long-term objective is to try to balance the company by moving into businesses we know something about," Bressler said in an interview today.

Last year the company reported sales of $4.93 billion, with $4.08 billion of that coming from the rail segment, while for the first six months of 1982, the railroad contributed $1.86 billion of the company's $2.05 billion in sales.

Burlington Northern is already in the timber, oil and gas, coal and mineral businesses and furthermore should know a fair amount about dealing in a highly complex regulatory environment, like that of the natural gas industry. Ironically, while the rail business increasingly deregulates, the natural gas and pipeline transmission business, the heart of the El Paso mission, remains in a muddled uncertain regulatory picture.

"We're not afraid of getting into a business with a lot of regulation attached to it," Bressler said. "It's really a regulated transportation business." There is little doubt of Bressler's commitment to the energy field since in 1982, Burlington Northern is already spending about $100 million on energy exploration and development, three times the comparable figure for 1980.

Nor does Bressler seem particularly fazed at having to get involved with California's often-difficult regulators. El Paso's 21,000 miles of pipeline, the first to bring natural gas to California, provide more than half of the natural gas used there, the leading natural gas user of the nation's 50 states.

Though the purchase, set for up to 25.1 million shares, which would give Burlington 50.1 percent of El Paso's stock, might not seem to pose antitrust problems in the view of Burlington Northern's management, it does raise several other questions. For instance, it comes on the eve of plans by the Securities and Exchange Commission to issue rules forcing the minimum time for keeping open a proration pool up to 20 days from 10 days.

The Burlington Northern bid sets a 10-day limit and Burlington Northern officials say timing of the announcement of the offer for El Paso had nothing to do with the new SEC regulations. Monday's board meeting was scheduled a year ago and an acquisition study was completed in October, they noted.

More serious, however, is the prospect of problems with the departments of Justice and Interior over coal-leasing policy. Two weeks ago, the Interior Department announced that it would halt leasing of federal coal deposits to energy companies affiliated with railroads.

According to the offering filing, Burlington Northern believes the Interior Department "would not approve the grant of additional leases." El Paso holds leases or interests in leases in coal deposits in Utah and North Dakota.

"There can be no assurance that there will not be a challenge through court proceedings or otherwise to the legality of BNI's becoming an affiliate of (El Paso) while (El Paso) holds federal coal leases, or that" either company "would prevail in the event of such a challenge," the filing said. Burlington says that if necessary, it is willing to establish independent management of the coal leases or sell them.

Analysts say that the risks make sense. El Paso's pipelines have an estimated life of 13 years, compared with an industry average of eight years. And energy prices are depressed at a time when rails are doing well. "You buy energy reserves when prices are depressed and the immediate to intermediate outlook is not so good," said Petery.