The American Trucking Association says United Parcel Service is doing what the trade group thinks is impossible: It is making a lot of money providing delivery service to the small towns and communities of America.

UPS's 55,000 plain, brown trucks with gold lettering are familiar sights all over the nation, even in remote areas not served by the U.S. Postal Service, Robert E. Smith, company vice president, boasted recently to Congress.

But the ATA contends it is this market that will be adversely affected by deregulation of the trucking industry, increaseing competition on the profitable big-city routes and leaving the smaller, less lucrative communities without trucking service.

ATA, which represents most of the regulated trucking companies, has mounted a major campaign against deregulation, using this as one of its prime arguments.

UPS is not a member of ATA, and it hasn't taken a stand on the overall trucking deregulation measures now before Congress, on grounds that the proposed changes wouldn't affect its operations. However, UPS has told Congress it does support open competition where its own business is concerned.

Unlike other companies regulatied by the Interstate Commerce Commission, UPS has made it a company policy never to protest the application of another company for new or expanded rights. Although the deregulation measures would increase competition in its field, Smith told Congress, "We do nt oppose it (competition) since it is already an accepted policy in our company today."

And UPS, contradicting ATA's contention that rural America will be victimized by industry deregulation, says it has no intention of abandoning those hamlets.

A good case can be made for UPS's stability in the industry. In the eyes of many consumers, UPS, which made more than 1.3 billion deliveries last year, has supplanted The Postal Service in delivering small packages.

The company even got a plug on television recently, during an episode of Barney Miller. A postal worker was jailed when it was discovered covered that his apartment overflowed with seven years' worth of undelivered mail. Asked about the famous motto promising delivery in rain and sleet and gloom of night, the postman replied, "Oh, that's UPS."

"Coverage or rural areas is one of the most attractive features of our service," Smith told the Senate Commerce Committee in December. "We provide this service today because we want to serve rural America; we asked for the right to do it, and we want to continue doing it."

A recent Transportation Department study of six small towns in three states -- selected by senators from those states on the Commerce Committee -- found that for the most part, the rural areas were being served by UPS and private carriers, not by the tegulated members, of ATA.

One reason UPS has grown so over the years, according to one knowledgeable transportation official, is its ability to promise shippers that it will deliver anywhere; for consumers and business, that's considered a major selling point. In addition, the official said delivery to rural areas can be easier than big-city deliveries, where drivers face traffic congestion, parking problems, and trouble locating addresses, requiring numerous trips to deliver a package.

Since its first days as a Seattle company, founded in 1907 by James Casey, UPS has expanded its territory to include every state. Today, the company employs 106,000 people and operates a transcontinental network of sorting terminals, tractor-trailers and other back-up services for the familiar brown trucks.

But UPS, doesn't have carte blanche delivery service and it can't go just anywhere. It's had its problems with regulation by the ICC, the agency responsible for regulating all interstate trucking services -- except those specifically exempted such as the hauling of agricultural commodities.

"Everybody in the United States has UPS service, but you can't always ship to the next state," says one transportation official. THE ICC has imposed a series of restriction prohibits Ups from handling shipments among Texas, Oklahoma and Kansas and portions of Nebraska, Missouri and Arkansas. An application seeking removal of that restriction has been pending at the ICC since July 1978.

UPS also is barred from making deliveries between Memphis, Tenn., and an area that includes Arkansas and part of Mississippi. Another restriction denies UPS service in either direction between Denver and the entire state of Kansas and the southern part of Nebraska.

All the restrictions were adopted to protect motor carriers already serving those areas.

UPS also is not allowed to accept more that 100 pounds from one shipper going to any one consignee on any one day. UPS has been trying since Novenber 1976 to have that removed.

The ICC last year did approve a UPS request to drop a restriction that had prohibited it from picking up packages from retail stores and carrying them across state lines to customers' premises. (Because the ICC restriction said "retail stores," UPS had made a distinction between retailers' stores and warehouses so large retailers with warehouses were able to take advantage of UPS services.) UPS's application for temporary authority to serve retailers on an interstate basis had been protested by the Postal Service on grounds that there was no immediate or urgent need for the service.