After months of sometimes arduous negotiations, the U.S.Urban Mass Transportation Administration (UMTA) yesterday gave approval to Metro to design an extension of the red line from Silver Spring to Glenmont.

The approval came in a letter from UMTA to Roy T. Dodge, Metro's assistant general manager for construction and design. While it permits Metro to resume work that was stopped last August, it does not guarantee the construction of the line.

The decision as to whether to quarantee construction will not be made until after a financing plan for Metro is constructed according to UMTA's C. Russell Scoville. Such a plan, UMTA has said on many occasions, must detail the source of the money that will be used to build and operate Metro beyond the presently funded 60 miles and must solve the problem of how to pay off revenue bonds that were sold for Metro construction.

The UMTA desicion yesterday is a landmark nonetheless because it constitutes at least an interim agreement in what has been one of the most protracted federal-located struggles since Metro construction began in 1969.

That struggle has involved a series of letters between Transportation Secretary Brock Adams and local officials, any number of meetings between UMTA and local staffs, at least one major engineering restudy of the Glenmont line, and an unusual consultants' report that UMTA ordered up to study another study.

Montgomery County officials, led by County Executive James P. Gleason Jr. and aided considerably by Maryland Transportation Secretary Hermann Intemann, insisted that the Glenmont line was an essential part of the county transportation plan. It would serve the dense Georgia Avenue corridor north of Silver Spring.

From the federal perspective; Glenmont is very expensive. The line would have to run almost entirely in a tunnel, deep in the hard rock under the Georgia Avenue corridor. Per mile, it would be most costly suburban segment in the proposed 100 mile Metro system. Federal approval is essential to the line, because the federal government would be expected to provide 80 per cent of the projected $347 million construction cost.

Gleason and other Maryland officials have beat back a series of attacks on Glenmont. In November 1976, when UMTA first ordered the region to restudy the system beyond 60 miles, Montgomery County succeeded in removing the Glenmont line from the study.

Last May, Transportation Secretary Brock Adams wrote that Glenmont should be included. Gleason, with the help of many other regional politicians, persuaded Adams to settle for an engineering analysis of the line in.

Out of that analysis came the first major chance in the design of Metro's underground stations. The Forest Glen station, it was agreed, would be smaller than those in operation today, and closer to the surface than originally planned. As a result, cost savings of $27 million were claimed by Metro and Montgomery County.

Still, UMTA had more questions. Requests for details on methods of construction the size of drainpipe, and other minute details increasingly infuriated local officials. "Metro is well on its way to going down the tubes." Metro board member Cleatus E. Barnett said at a board meeting in December. Barnett represents Gleason. Metro genral manager Theodore Lutz was dispatched to meet with UMTA Administrator Richard Page to see if the rough edges couldn't be smoothed.

UMTA also asked Metro to study several different construction techniques for both the Wheaton and Forest Glen stations. Metro's engineers submitted a report concluding that the design growing from the engineering analysis was the cheapest.

UMTA then spent $2,885 to hire an engineering consultant from London Transport to restudy the engineering report. That consultant spent 11 working days here, wrote an 18-page report that contained no specific cost estimates, but suggested saving could be made with different construction techniques. When Metro asked for the report, it received a version with several paragraphs blanked out.

The paragraphs, obtained by The Washington Post, suggested generally that pilot construction might be tried to determine which method was cheapest. Such proposals were never made to Metro, Dodge said yesterday.

Scoville said the paragraphs were not given to Metro because they contained "unsolicited advice" that went beyond specific engineering discussions.

Had Metro's design schedule continued uninterrupted, Dodge said yesterday, Glenmont drawings would have been completed last month. Now, with the new design, it will be August 1979 before they are completed. The new design, he said, will cost $2.5 million to $3 million. The original design had cost about $3 million.

In his letter to Dodge yesterday, Scoville said that the Metro design for the Forest Glen station was accepted. He left to Metro and Montgomery County the selection of one of four options for construction and development around the Wheaton station.