It is increasingly likely that the Washington Metro subways originally planned 100 miles will not be completed for about 10 years.

Metro board members, who are seeking final local, state and federal approval for a new financial plan to construct part or all of the system's final 40 miles, list "late 1987" as the probable completion date. The final total cost is estimated at $6.9 billion.

The system could be completed as much as two years earlier, and for $200 million less, if Metro's preferred option in the financial plan is adopted by the federal government. That option, however, requires enormous federal expenditures in the first two years - the same years in which President Carter hopes to curb inflation by controlling federal spending.

Sixty miles of the Metro system are fully funded. With the opening of the New Carrollton line tomorrow, 31 miles will be in full operation. Several other segments will open within a relatively short period of time. Here is the status of each uncompleted Metro segment: RED LINE

Dupont Circle to Van Ness Center - Fully funded and under construction: Operation date: early 1983. This segment may open in two sequences, with the first including stations between Van Ness Center and Grosvenor.

Silver Spring to Glenmont - Final design work is fully funded; there is no money for construction. Operation date: early 1987. BLUE LINE

National Airport to Huntington - Fully funded and under construction. Operation date: early 1982.

Stadium-Armory to Addison Road - Fully funded and under construction: operation date: late 1980. ORANGE LINE

Rosslyn to Ballton - Fully - funded and under construction. Operation date: Late 1979.

Ballston to Vienna - Not funded. Some right-of-way work is being done by the Virginia Department of Highway and Transportation as part of Interstate Rte. 66 construction. Operation date: early 1983. YELLOW LINE

Pentagon to Gallery Place - Partially funded and under construction.Most construction work is completed, but about $10 million to $12 million is needed for track and signal equipment. Operation date late 1981.

King Street to Van Dorn Street - not funded. Operation date: late 1983.

Van Dorn Street to Franconia/Springfield - Not funded. Operation date: late 1984. GREEN LINE

Gallery Place to Anacostia - Partially funded and constructed as far as Waterfront station, unfunded from Waterfront to Anacostia. Operation date: late 1983.

Anacostia to Rosecroft - Not funded. Operation date: mid-1986.

Gallery Place to Columbia Heights Not funded. Operation date: mid-1985.

Columbia Heights to Greenbelt - Not funded. Operation date: Late 1987.