For several years, Alexandria officials have watched with frustration as Metrorail tracks stretched closer to the city and the date for the first trains on those tracks slipped further away.

The five-mile extension of the Blue Line from National Airport to Alexandria was supposed to open late this year. Nine months ago delays in delivery of new train cars forced Metro officials to move to next fall the date for arrival of the subway in Alexandria.

Now even that date seems in doubt. Metro, concerned about train breakdowns, reliability of service and the size of its fleet, is considering plans that would use at least two dozen of the new cars, expected to begin arriving next year, to improve service on existing lines.

That could delay service to Alexandria until as late as June 1984 -- a postponement that has some Alexandria City Council members fuming over what they describe as Metro's "cavalier" attitude toward the city.

"I think we're getting jerked around by WMATA," said Vice Mayor James P. Moran, referring to the Washington Metropolitan Area Transit Authority, or Metro. "If this was a business enterprise, no executive would have stood for these constant delays. Every year goes by and they invariably notify us of another delay or additional cost. You reach the end of your rope. You just keep looking for that goal beyond the rainbow, but instead we just keep getting rained on."

"We've paid out about $43 million for Metrorail," said council member Donald Casey, "and we still don't have any service."

"It bothers me terribly," agreed council member Margaret B. Inman at a council session last week. "Alexandrians have paid a very heavy proportion of their taxes for Metro. We have contributed so long. Why are we being told again that we come last?"

The four Metro subway stations in and south of the city are finished. The rails at King Street, Braddock Road, Eisenhower Avenue and Huntington station, which form a north-south arc along the western edge of Old Town, are complete. The rails have been electrified since early this year, and Metro has been running tests since then. To those near the stations, the test cars braking and pulling out of the four new stations have become a familiar sight.

One reason for the delayed delivery of the new Metro cars was a strike by the brake manufacturer. But that strike has been settled, which means that the 94 cars on order, as well as 100 more, should be delivered at a rate of two a week starting sometime next year, according to a Metro spokesman. Among them should be the approximately 28 cars needed to start up Alexandria service.

Full speed ahead, then? Not exactly.

The new wrinkle, according to Alexandria Assistant City Manager Clifford Rusch, is the unreliability factor. Metro trains have been breaking down at record rates and causing delays in service, and Metro officials would like to increase the size of the subway fleet. Ideally, spare cars should number about 15 percent of the fleet, but Metro has been operating with considerably fewer, according to Metrorail scheduling engineer Donald Hamburg.

Transit payments by Alexandria have increased steadily over the past few years, from $3.3 million in 1978 to $5.7 million last year. At the same time, the percentage going for bus service has decreased steadily as the city has phased out bus lines. Next year, the city bill for rail construction and service alone will be $1.14 million.

"We've paid through the nose on this thing, and the least we could do is get some commitment from them," Vice Mayor Moran said at last week's council meeting.

"Right on," agreed his colleagues.

Last week, at its first regular meeting of the fall, the council decided to send Metro a letter. "Metro is looking at a lot of service options," said Assistant City Manager Rusch. "We want them to know we'll be watching."

But at least one council member has more faith in personal lobbying than in pen and paper -- even if the letter carries the city seal.

"I don't think a letter will do much," Moran said after last week's meeting. "What this will do is give Chuck Mayor Charles E. Beatley Jr. a green light to go down there and kick a--."