Congressional use of free franking mailing privileges is expected to take a 40 per cent jump during the impending campaign period to a half billion deliveries.

This estimate by the U.S. Postal Service means that roughly eight deliveries could be made for every postal addressee in the United States. The prediction covers the fiscal year ending in October, 1976, when the bulk of next year's campaign activity will be conducted.

In the nonelection year of 1979, the volume franked mail is expected to go down to fewer than 400 million pieces.

Franked mail -letters, pamphlets, books and other material sent by senators and members of the House at no cost to themselves individually - is intended for regular office business.

But the increased volume in election years is a well-documented pattern. In fact, at a recent postal rate hearing, a Postal Service official called franked mail "unique among all mail classes" in that seasonal factors used for forecasting volume "are for pairs of years . . . to recognize any effect that may follow from the biennial cycle of congressional elections."

Not surprisingly, direct mail has become an increasingly important tool in election campaigns.

The frank is another of the perquisites that senators and House members have accumulated over the years.

Its use will rise to record levels this year because, under the tattered banner of official need, both houses of Congress in recent years have given boosts to allowances related to franked mail.

On the surface, many of the increases appeared innocent - an increase in a senator's paper allowance; a $5,000 constituent communications allowance for House members: transfer of clerk hire to computer expenditures, and a limit on the number of postal-patron mass mailings a House member can make.

A closer look shows that each move fueled the growth of franked congressional mailings.

The latest House revision that will go into effect Jan. 1 limits the amount of so-called "occupant" or postal-patron mail a member can send. These are mass-mailed letters sent to all residents in a district where the member does not have the names of the addresses.

Before the revision, a member hypothetically could make as many such mailings as he or she pleased. However, only a handful of members did as many as six, and most did one or none.

Nevertheless, the revision made the equivalent of six district-wide mailings the limit. It went further, however, saying that a member was entitled to make "occupant" mailings totaling six times the number of postal patrons in his or her district.

Thus if a member has 100,000 postal patrons in his or her district, the member will be permitted to send 600,000 franked "occupant" pieces a year. How those mailings are divided will be up to the member.

One way to measure how members value such mass mailings came up recently when a public financing bill for House election campaigns was taken up in the House Administration Committee.

Under a committee-drafted bill, a candidate who raised $10,000 in contributions of $100 or less would be given one mass mailing - at government expense - to every voter in the district.

The community valued that mailing at $25,000.

Under the House revision, the only rules a member has to worry about require such letters to be sent third-class rather than first-class, and stipulate that they cannot be sent less than 60 days before a primary or general election.

Postal officials point to this new "occupant mail provision as one reason for their sharply increased projection of franked mail.

Capitol Hill aides say members will be more tempted to use mass mailings now that the limit of six district-wide mailings has been established. They also point out tht they can take specific areas in the district and mail to postal patrons there more than six times, as long as they don't make that number of mailings through the entire district.

The aides also note that the new House limit does not apply to franked mailings where the member has the name of the addressee. Those mailings are only limited by the amount of official funds a member to pay for the printed matter that is transmitted.

On the Senate side, the House action has created new interest in postal-patron mailing. By tradition, the Senate has shunned that device - so much so that senators currently are barred by postal regulations from using it.

Earlier this year, however, the Senate Governmental Affairs Committee asked the Postal Service to review that regulation and amend it with regard to senators if it found such action was permitted by law.

As of now, senators are limited in their use of the frank only by the amount of paper available to them under their paper allowance system.

It 1975, the Senate raised that allowance, giving each member one sheet of paper a year for each state resident 18 or over.

It didn't sound like much. But a senator from California, who before the increase was able to mail under frank 2 million pieces a year, is now able to send 14.5 million.

That increase permitted Senate franked mail to increase 167 million pieces a year.

Other recent moves that have affected franked mail include:

In 1975, House members each got a new $5,000 constituent communications allowance, which was to be used on producing an official - not political - newsletter twice a year. Where many members once financed mailing newsletters with campaigning funds, these were to be sent out under the frank.

That same year, members got authority to spend $1,000 a month from their clerk-hire allowance to purchase computer services. Many members used that money to hire direct-mail specialists and establish computerized mailing programs.

In 1976, House expense allowances were made transferrable so that if a member ran out of money for newsletters from the communications account, he or she could supplement it with funds from unused travel or home office rental money.

Both houses have taken one step that could limit - to a degree - franked mail. Beginning in January, only material paid for out of official funds can be sent as part of franked mass mailings. Such mailings are defined as 500 letters with substantially the same content.

In the past, members have been able to use campaign funds to print or prepare material then sent out under the frank.

The Senate Republican a Campaign Committee recently asked the Federal Election Commission to approve its using campaign funds to pay for official mailings by senators.

The House, indirectly, currently prohibits that. Its new rules say that anything paid for by campaign funds is automatically political, rather than official, and thus is barred by law from being carried under the frank.

Four years ago, Common Cause, the citizens' lobbying organization, instituted a lawsuit aimed at stopping mass mailings under the frank by members of Congress.

Common Cause counsel Kenneth Guido said recently that in the suit he was "trying to show franked mail is being used to promote incumbents' election campaigns to the detriment of challengers."

Through the suit, Common Cause hopes to have some limits put on the amount of mass mail members can frank. At the rate the use of the frank is growing, some inhibitions apparently are becoming necessary.