In the basement of the Dirksen Senate Office Building, four web printing presses work two shifts a day, grinding out, in an average week, 3 million newsletter, special interest communications and press releases bound by franked mail to some senator's constituents.

In air conditioned rooms down the hall in Dirksen, the Senate's IBM 168 computer spits out names and addresses on gummed labels from specially coded lists stored in its memory banks for each Senate office.

The presses, the computer, paper, franked postage and mailing services are all paid by the taxpayer. No one can say for sure how much the while operation costs.

Everyone agrees on one thing, however. With the advent of computerized address lists, the direct mail operations of most senators and congressmen - which ran $51 million in postage alone in fiscal 1976 - are on the rise.

Two years ago, For example, the Senate raised its paper allocation for each member. Under a Rules Committee edict, each member was allowed one sheet of paper a year for each state resident 18 years old and over.

It didn't sound like much. But a senator from California, who before was able to mail 2 million pieces a year, could threreafter send 14.5 million.

Overall, the 1975 paper allotment rule change permitted a yearly increase of 167 million pieces of mail, according to Chester Smith, the Rules Committee chief counsel.

Under rules set up by the Senate Service Department, which does the printing, senators from big states like California. New York and Illinois can send out 900,000 copies of a two-page newsletter each month.

Senators with smaller populations are allowed fewer copies, but even the smallest state is permitted 375,000 copies of a two-page newsletter a month.

Members have taken to calling this activity constituent communications.

Common Cause, in a lawsuit initially filed four years ago, has charged that franked newsletters and other mass congressional mailings are unlawful disbursements of public funds for political purposes.

Through depositions and subpoenaed records, the Common Cause lawyers have compiled an enormous amount of data on franked mailing in both the House and the Senate. They have not gotten all they wanted.

Tomorrow the lawsuit may take a different turn.

A lawyer for the U.S. Senate, Cornelius Kennedy, is expected to bring word to a court hearing that the Senate will refuse to permit the administrative assistants of all 100 senators to testify on their mailing practices.

The Senate also apparently will not turn over in the court compute records of 1972 mailings and the number of pieces that have been sent under frank over the past five years.

Since subpoena were issuef for computer data in 1974 and the AA's testimony over a year ago, lawyers on both sides of the case expect the three-judge federal court panel hearing the case to order the Senate officials involved to be cited for contempt.

A resolution of the Senate is required before any employee can testify in court. None has been approved. Therefore a court contempt citation would change the franking case into a constitutional test of congressional immunity.

An aide to Sen. Lee Metcalf (D-Mont.), chairman of the Ad Hoe Committee on Legislative Immunity, which has supervised the Senate handling of the suit, said last week, "This is likely to become a significant case before it is through."

For Common Cause lawyers, however, the congressional immunity question is only a diversion to their making legal arguments against continuation of franked mass mailings, which even now are illegal if used for personal or political ends.

Depositions in the case taken by Common Cause include the following accounts:

A memo written by Joyce Baker, a former employee of Sen. John Tower (R-Tex.), described franked mail sent in June, 1972, to special interest groups and to welcome new state residents and special interest groups in Texas and said it was considered part of Tower's re-election campaign that year.

Baker also disclosed that members have used campaign funds to pay for additional printing by the Senate Service Department when paper allotments were exceeded.

Lee MacGregor, a direct mail advertising specialist, testified that he worked for Sen. Robert Griffin (R-Mich.) and other senators for periods of two months or more to set up direct mail programs. In the case of Sen. Jacob Javits (R-N.Y.) MacGregor targeted mailings to areas where Javits had not done well in prior elections.

A staff aide of the House Republican Congressional Campaign Committee testified that in 1974, GOP House Freshmen and incumbent Republicans from marginal districts were given more money for direct mail programs than members without serious opposition. House members at that time did not have a free paper allotment and printing system comparable to the Senate and had to pay for newsletter printing.

"Exhibits supplied by a direct mail specialist showed that individual senators were building up mailing lists with such categories as progessions, campaign volunteers, gun owners, pilots, political party, sex, age, veterans and contributors.

The specialist said under questioning that he had advised members that "mailing objectives should be established to provide for a mailing to some group each week."

The Senate's new code of conduct incorporates changes in franking practices. For example, campaign funds can no longer be used to supplement the costs of printing franked mail pieces.

The new code also requires that all material carried under the frank be produced in the Senate - another effort to ensure that official, not campaign, material is used.

Common Cause lawyers, however, are said to believe these moves do not address the real problem - that any congressman's mass mailing to constituents who have not requested it is a political rather than official function.