Western Union Corp. is in trouble, and while some analysts joke that problems with the telegram business began when Alexander Graham Bell invented the telephone, nobody at the company is laughing.

After a continuing decline in the rate of growth of its telegram and telex businesses, Western Union embarked on an ambitious diversification program several years ago. But company officials concede they lacked the financial resources and management talent to support that effort.

Amidst mounting losses and a shortage of cash, which the company needs to promote its new Easylink electronic mail subsidiary, Western Union has eliminated dividends on its stock; announced plans to sell two subsidiaries, reduce employment by up to 10 percent and cut wages 10 percent; lost a $100 million line of credit with eight banks, and replaced its chairman.

"We are taking vigorous steps to reduce expenses in all areas," said Western Union spokesman Warren R. Bechtel. "We have tried to make it clear that the company has got to narrow its focus. We are obviously in a difficult situation, and we are dealing with it forcefully."

Analysts said the company is betting its future on Easylink, an electronic mail subsidiary. The high cost of promoting that business is hurting profits, but the company hopes the investment will pay off in the future as the concept of terminal-to-terminal communication gains acceptance. The company is spending about $45 million this year to promote Easylink, which will lose more than $24 million in 1984.

As the company has suffered, its stock price has plunged from a 52-week high of 39 3/4 to yesterday's close of 10 3/4, up 3/8. With its stock price this depressed, the company has a market capitalization far below its net worth, making it an interesting takeover target for an investor willing to buy all of the company's stock and sell the assets.

"The lower the stock price goes, the more likely it becomes that someone will buy the whole company," according to a research report by Prudential-Bache Securities. "Western Union is in a bind and must sell off assets and/or the whole company from a very poor bargaining position," the research report said.

But some analysts speculate that the company's new chairman, T. Roland Berner, is announcing all of the bad news to give the company the leverage it needs to convince union and non-union employes to take pay cuts. They said Berner is an opportunist who might be making the most of the bad news by carefully disclosing all of the company's problems to the press.

Berner, who took over as chairman of the company in August, also is chairman of Curtiss-Wright Corp., an aerospace parts company. During 1981 and 1982, Curtiss-Wright bought 4.4 million shares in Western Union, about 18.5 percent of the company, for about $31 a share, Western Union's Bechtel said. Analysts said Berner's involvement in managing Western Union is aimed at restoring the value of that investment.

One of the company's newest ventures is Airfone Inc., an airplane-to-ground telephone service that operates on commercial flights. Western Union owns 50 percent of the company, but its future is uncertain since the Federal Communications Commission voted last month to deny the company permanent access to frequency space.

Western Union also recently entered the long-distance telephone business.

"There have been a number of rumors suggesting the company was in an extremely difficult financial position and that something radical might happen," said Steven G. Chrust, an analyst with Sanford C. Bernstein & Co. "The market with the greatest potential is the electronic mail business and that is what they are emphasizing, but I don't know. . . . The debt burden is very substantial, including their unfunded pension liabilities. . . . It is hard to be optimistic."

The company has retained the investment banking firm of Salomon Brothers to sell a subsidiary it bought in 1982 -- E. F. Johnson Co., a maker of mobile radio telephones -- and its own field services unit, which repairs and installs communications equipment.

Amidst all the uncertainty about the company's future, Standard & Poor's Corp. lowered its rating on some of Western Union's debt. "Major investment in new domestic network communications services are an unexpectedly large drag on profitability reflecting heavy start-up costs, competition and slowness of markets to develop," S&P said.

"Despite some bright spots, other traditional businesses are suffering major cost increases and narrow margins. . . . As a result, profits are being supplanted by operating losses, cutting fixed charge coverage and cash flow to a very weak level.

"Recent cancellation of a newly negotiated $100 million bank credit facility triggered suspension of preferred dividends, severely restricting external financing flexibility," S&P said.

The company's principal source of revenue continues to be its Telex business, described by company spokesman Bechtel as "the world's standard for record communications.

"When it comes to non-voice business communications around the world, Telex is it and will be for some time," Bechtel said. He added that the company only recently was permitted to enter the international Telex business. Telex accounted for about 29 percent of its $1 billion in revenue last year.

One Western Union employe who works for the company in Virginia said she was very upset about the cuts in pay and medical benefits. She said morale is low, and that several employes in her office are looking for other jobs.

She said the company did not hold a special meeting to disclose the cuts.

Instead, she said, "They sent a Telex last Friday."