The number of inmates at the Montgomery County jail--a facility designed to house no more than 272--has hit an all time peak of 438, and county officials took steps yesterday to provide relief.

The County Council tentatively approved a $6.5 million, 120-bed jail expansion that would be completed in 1986 plus a $500,000, 20-bed expansion of the county's prerelease center, where inmates serve the last six months of their sentences. A final decision whether to fund the projects is expected in May.

And County Executive Charles W. Gilchrist called on the council to agree to hire 10 additional corrections officers, declaring that the "unforeseen increase" in the number of inmates "has severely limited the Corrections Department's capability to supervise" at the jail on Seven Locks Road in Rockville.

Jail officials are now housing two inmates in cells designed for one and some prisoners sleep on mattresses on the floor.

Overcrowding has also increased tension, which officials say prompts guards who feel unable to cope with the situation to claim more sick leave.

A recent county report said that "if overcrowding persists, chances are greater for disturbances and riots."

County Corrections Director Gary Blake said Washington area crime trends appear to be responsible for the rise in the number of inmates. He said most county jail inmates in the '70s were 17 to 26 years old, but the depressed economy has led criminals to remain active longer.

"People aren't 'burning out' on crime the way they used to," he said. "There are still as many people at 18 that we see, but criminals are continuing right into their 30s. They start out with minor crimes, but they come back for increasingly serious offenses."

Another trend is the growing proportion of inmates who are not county residents. In 1976, 60 percent of the 218 inmates then at the jail were from Montgomery; now the figure has dropped to 49 percent. The percentage from the District of Columbia is 22 and from Prince George's 13 (more than double the 5.8 percent in 1976). A jail report last month blamed "increased mobility and the advent of Metro" for the increase of inmates from other jurisdictions.

Blake said suspects from elsewhere are far less likely to be released on bond than persons who live in Montgomery, adding to the number incarcerated.

Other factors cited to explain the crowding are an increase in the number of women jailed, imposition of longer sentences and sentencing of greater numbers of so-called serious offenders to serve terms locally rather than in state facilities, which have their own overcrowding problems.