Dallas has joined the list of automobile-choked western cities that are willing to tax themselves to build a rail transit system to ease traffic problems.

More than 58 percent of the voters in Dallas and 20 surrounding municipalities Saturday approved a 1-cent sales tax and endorsed a long-range transit plan that was supported vigorously by downtown business interests that have been seeking stronger transit there for more than a decade.

The plan concentrates on doubling the Dallas bus fleet of 560 by 1986, then building a 160-mile rail system to be completed in stages at a cost of $8.75 billion (in 1982 dollars).

Only 3.4 miles of the downtown rail system would be in subway. The rest would be on the surface or elevated and would follow existing rail rights of way.

If Dallas completes that grand scheme it will have a achieved a Texas-sized ambition. Fred Curry, chairman of the Dallas Transit Board, called the election result "a quantum leap forward for urban mass transit in general."

"This represents a philosophy on the part of the city of Dallas that what many people think of as impossible to do is in fact possible and the city of Dallas has decided to do it," he said.

The grand plan even has a zippy name, DART, for Dallas Area Rapid Transit. Like transit plans everywhere, it also has opponents who will undoubtedly be heard from again.

Dallas businessman Dewayn Dallas said that "Dallas has just saddled itself with a giant indebtedness, and they won't come out of it without some real financial scars. I think it's a financial Dunkirk myself."

The same argument has been heard again and again about systems such as Washington's Metro and Atlanta's MARTA, both of which have been extremely popular even if extremely expensive.

Metro, for example, was supposed to cost $2.5 billion when it was designed in the mid-1960s. Now Metro planners will not publicly estimate the final cost, but back-of-the-envelope figures exceed $11 billion if the planned 101-mile system is completed.

Metro, MARTA and new systems in Baltimore and Miami use what is known as "heavy-rail" technology, meaning that they are built to high-speed mainline railroad standards.

Dallas is talking about "light rail," the modern version of a trolley, where the rail and the rolling stock are lighter and speeds are somewhat slower.

Light rail systems are rapidly gaining popularity. A major system is under construction in Buffalo, and systems are operating with great success in San Diego and the Canadian cities of Edmonton and Calgary. Light rail systems are also in the serious planning stages in San Jose and Portland, Oregon.

Houston, Dallas' competitor to the southeast, recently shot itself in the foot after launching an ambitious transit program by passing a 1-cent sales tax in 1978 to finance it. But Houston voters then rejected a bond issue for the planned rail system, effectively killing the program. Houston community leaders and transit officials are regrouping.

Jack R. Gilstrap, executive vice president of the American Public Transit Association, said yesterday that "The emergence of the light rail concept provides considerable cost savings over subways." He added, "We are also seeing the willingness of citizens to inhibit automobiles."

Dallas' plan has several interesting features, including the proposition that it will be built completely with local funds, assuming that there are no federal funds available.

However, Dallas undoubtedly will seek federal assistance under existing transit grant formulas for its bus fleet expansion, a plan that requires major garage and equipment purchases, most of which are eligible for federal aid.

Further, Texas congressmen played a significant role last November in pushing for a 5-cent-a-gallon increase in the federal gasoline tax after winning Reagan administration agreement that some of that money could be used for new rail transit systems.

At some point, it seems inevitable that Dallas will seek federal rail aid as well, just as San Diego has done for proposed additions to its self-financed trolley system.

The Dallas task force that pushed through the proposal paid close attention to the Houston experience and made certain that Dallas voters knew when the election was going to be and what the benefits of mass transit would be.

However, Dallas, too, will have to go back to the voters for bond approval when its transit plan is ready to implement.

The task force launched a $1 million campaign that included mass mailings, yard signs and a 65-line phone bank. The campaign also included a pledge used by Atlanta's business community years ago to get MARTA started: a promised fare reduction. The basic transit fare in Dallas will go from 70 cents to 50 cents when the sales tax takes effect Jan. 1.