Theodore C. Lutz, a 33-year-old financial whiz who presided over the successful opening of 26 miles of Metro subway and convinced both local and federal governments that Metro could work, announced yesterday that he will resign in April after 2 1/2 years as Metro general manager.

Lutz, who earns $58,000 yearly, said he has no new job and no firm commitments He told the board his decision was "painful and difficult," but in his letter of resignation said "I look forward to an opportunity to renew depleted intellectual, emotional and physical resources."

He said in an interview later that he was "burned out" by a job that had required unrelieved attention since he assumed it Nov. 8, 1978. Since that time, Lutz has taken only one break of more than four days' duration -- a seven-day vacation this past Christmas.

Jerry A. Moore Jr., acting Metro board chairman, deferred formal action on Lutz's resignation. "I don't think any of us know what to do at this time," Moore said. "The board will have to meet and decide how to proceed."

There was no immediate speculation on possible successors. However, several board members said they felt anyone holding the job would have to have a good understanding of both the federal establishment and the unusual local political coalition that makes up the Metro board. The board is composed of two members and two alternates each from Maryland, Virginia and the District of Columbia.

Board members seemed generally surprised that Lutz chose yesterday to make his announcement, although he had informed Moore about a week ago that he was planning to resign.

"You have left us dumbfounded," Moore said. "You've done a tremendous job for the people of the region."

Lutz will leave Metro with its political support intact but its financial future unresolved. He noted yesterday that by the end of April both the Maryland and Virginia legislatures will have concluded their sessions and the important (for Metro) congressional appropriations hearings will have been completed.

During his tenure Metro was plagued with a number of major problems, including start-up problems on the subway cars. A flood caused by a construction accident closed the system, and Metro's bus drivers, mechanics and train operators went out on a week-long wildeat strike last summer, crippling the city during a heat wave. All those problems were overcome.

Lutz started the Metro job six weeks after the U.S. Department of Transportation ordered local area governments to restudy several uncompleted lines of the planned 100-mile subway system. It was clear at that time that there was significant local and federal support to truncate the system, which was supposed to cost $2.5 billion to build in 1968 but is now estimated to required $7 billion.

While that study was proceeding, the subway was growing from four operating miles to 30 and was building a substantial constituency among its steadily increasing numbers of riders. All local governments have reaffirmed their commitment to completing the system and the federal government has said it now supports that local goal.

Lutz reorganized the Metro staff during that time to shift its emphasis from constructing a subway system to operating a combined, full-service bus and subway network.

He lobbied local politicians hard to put up the subsidy money that was needed to open the subway at nights and on Saturdays, and thus increase its popularity even more. He is trying to get Sunday service started next fall.

Lutz also spent hours on Capitol Hill working for national transit legislation and for stop-gap appropriations to pay Metro's bills while long-term financial commitments were negotiated.

Lutz traveled to Richmond and Annapolis to lobby the legislatures for Metro aid, and spent many lunch hours speaking to civic groups and explaining Metro's problems.

Metro's fares had to be renegotiated twice during Lutz' tenure, and the painful process of allocating the Metro operating revenues and deficits to eight different cities and counties in the region required endless meetings and hours.

"If I made one mistake in taking this job," Lutz said to a reporter in the midst of the transit strike last July, "it was that I failed to negotiate myself a long sabbatical. I haven't read anything but transit reports and financial statements for months."

Lutz was also under pressure at home to cut his hours on the job. A new Lutz, Christopher Compton, age 5 months, has added to those pressures. Lutz' wife, "Willa, has had him under pressure for years to slow down," a close Lutz family friend said yesterday.

Lutz came to Metro from the U.S. Department of Transportation, where he had been deputy under secretary for four years. Before that he worked in the federal Office of Management and Budget on D.C. and area matters, including Metro.

Lutz' successor will be Metro's third general manager. The first, Jackson Graham, a master builder with a Corps of Engineers background, held the job for eight years.

"When Graham left I thought he was irreplaceable," one board member said yesterday. "I think the same thing about Ted Lutz now. I'm very pessimistic that we can find somebody else with those skills."