The Federal Home Loan Bank Board is expected to appove a pilot program today that will allow District savings and loan asssociations to branch into the lucrative suburban market, savings industry sources said last night.

Long sought by the city's S&Ls, who are unique in the nation in their restriction to a territory totalling 26 square miles, the appoval for interstate branching would apply only to this metropolitan region. City lenders have maintained that they have suffered from not being able to do business where the bulk of the population lives.

The bank board action undoubtedly will touch off lawsuits by thrift institutions in the suburbs, who do not welcome the competition from big urban institutions and who have maintained all along that such a policy would be illegal. Although there is no law against branching across state lines, it has been prohibited under regulatory policy since the 1930s.

Three S&Ls here-Perpetual Federal, National Permanent Federal and Guardian Federal-have branches in both the District and Maryland that were set up before the policy was established. Perpetual and Columbia Federal S&L have sought permission in recent years to open offices in Montgomery Country.

Bank board Chairman Robert McKinney has said previously that the results of any areawide branching here would be monitored to ascertain the implications for metropolitan branching in other parts of the country. Studies by the S&L regulatory agency have showed that D.C.-based S&Ls could expect to pick up $500 million in new deposits in five years with suburban branches. Of that, $125 million would be made available for the inner city and the balance for home mortgages in the suburbs, McKinney indicated.

Although a number of thrift institutions in Maryland and Virginia have not spoken for or against the branching plan, most are known to oppose it. However, ther were unconfirmed reports last night that one major S&L in maryland is seeking to acquire a Virginia S&L, which the pilot program would permit. Suburban institutions also could open offices in the city under the pilot program.

In addition, if D.C. savings associations are permitted to branch to the suburbs, there will be renewed pressure from the city's banking industry for legislation to permit them to follow suit because thrift institutions are growing conpetitors for a variety of financial services.

A major factor in the decision to modify branching laws here is the Carter administration's mandate to the savings and loan industry to provide additional mortgage money for rebuilding the nation's inner cities, sources have indicated.