The new Express Mail stamp being put out tomorrow at San Francisco is amply chunky but not the biggest United States issue -- it is dwarfed by the newspaper stamps of 1865 -- but it is in a class by itself as the most costly postage stamp in the nation's history.

With a denomination of $10.75 and a design that packs more punch, it has dethroned the previous titleholder, the $9.35 stamp that held the championship from mid-August 1983, when the costliest classification made its appearance, to the present. The new titleholder's crown may be shaky, however, for already there are reports that a dark horse of over $12 is in training to take over next year.

Like its predecessor, the new stamp is being issued in booklets containing one pane of three stamps. It is being sold over the counter individually and in booklets, and should be available at major post offices.

The stamp is intended primarily for use on items weighing up to two pounds that are sent via Express Mail Next Day Service but is also valid for postage on other types of mail.

The $9.35 stamp was introduced to accommodate increased use of the service and provide users with a convenient way of applying postage, especially those using collection boxes for Express Mail.

The two Express Mail stamps were designed by the Postal Service's advertising agency, Young and Rubicam of New York, and are alike in basic design concept but with salient differences. Both have the American bald eagle as the symbol of the swift overnight service, both have the backdrop of outer space and both have the impressive denomination in bold display across the bottom.

The earlier stamp had a side view of the eagle's head blocking out a segment of a full moon against the background of the darkness of space. In the new stamp, the bird looms larger and more powerful because it is facing more toward the viewer, who is really getting the eagle eye and a close peek at the beak because the full moon has now become a half moon. In addition, the eagle's body is now in clear view along with the raptorial beak, largely because the background of space has taken on a roseate hue.

The stamp has been produced by gravure in five colors: yellow, cyan, black, magenta and a special pinkish red. A five-digit plate number appears at the top of each pane of stamps in the booklet.

Collectors of first-day-of-issue cancellations have a deadline of May 29 because of the customary 30-day grace period for placing orders and the usual alternative ways of ordering covers.

Collectors acquiring stamps: Those affixing stamps on envelopes, which must bear return addresses, should send the covers to Customer-Affixed Envelopes, $10.75 Stamp, San Francisco, Calif. 94188-9991.

Postal Service affixing stamps: Those preferring full processing of covers by the USPS should send their envelopes, with return addresses, to $10.75 Stamp, Postmaster, San Francisco, Calif. 94188-9992. The cost is $10.75 for each stamp affixed on a cover. Personal checks are accepted. Cash is highly inadvisable. Payment by postage stamps is refused.

The new coil stamps, a 10.1-cent showing an 1890s oil wagon and a 12.5-cent depicting an 1880s pushcart, have been put out in Oil Center, N.M., as the 17th and 18th issues in the ongoing Transportation series.

The 10.1-cent denomination represents the rate for bulk third-class mail presorted to the five-digit zip code. The 12.5-cent denomination represents the basic rate for bulk third-class mail.

The stamps have been printed by intaglio with the oil wagon in blue and the pushcart in olive green and have been issued in coils of 500 and 3,000. There is a single-digit plate number that appears every 52nd stamp.

Collectors of first-day cancellations must send in their orders no later than May 18 -- orders must be postmarked by that date -- and use one of two ways of ordering.

Those acquiring stamps: In addition to the 10.1-cent oil wagon stamp, collectors must add at least 11.9 cents additional postage on their envelopes, which must be addressed, to fulfill the first-class rate for letters. For the 12.5-cent pushcart stamp, cover collectors must add at least 9.5 cents postage to their envelopes. Orders should be sent to Customer-Affixed Envelopes, Oil Wagon Stamp -- or Pushcart Stamp -- Postmaster, Oil Center, N.M. 88266-9991.

Those preferring full processing by the Postal Service should send their envelopes, with return addresses, to Oil Wagon Stamp -- or Pushcart Stamp -- Postmaster, Oil Center, N.M. 88266-9992. The USPS will apply one 10.1-cent stamp and one 12.5-cent stamp to meet the first-class rate. The cost is 23 cents per pair of these stamps applied on a cover. Personal checks are accepted.

The following May dates in italics are the currently scheduled first days of issue by the United States, the United Nations and Canada.

United States -- 3: Nonprofit-rate 6-cent stamped envelope showing "Old Ironsides," the USS Constitution, Boston, Mass. 21916; 11: Rural Electrification Administration 50th anniversary 22-cent commemorative, Madison, S.D. 57042; 15: Official Mail 14-cent sheet and 22-cent coil, Washington, D.C. 20066; 21: a 36-cent Travel aerogramme, Washington, D.C. 20066; 25: Ameripex '86 stamp on stamp 22-cent commemorative, Chicago, Ill. 60607.

United Nations -- 10: Six definitives and postal stationery, U.N. Postal Administration, Box 5900, Grand Central Station, New York, N.Y. 10163.

Canada -- 6: A 32-cent commemorative for Northwest Rebellion Centennial, Philatelic Service, Canada Post, National Philatelic Centre, Antigonish, N.S. Canada, B2G 2R8.