The first major step in creating a domestic natural rubber industry began today when Goodyear Tire and Rubber Co. representatives began planting 15 acres of guayule seedlings near here on Arizona State University farmland.

The planting of the seedlings, which will grow into desert shrubs that produce large quantities of rubber, marks the start of a plan to lessen U.S. reliance on foreign rubber supplies, company officials said. Representatives from the university, Goodyear, three Arizona Indian tribes and a local research corporation are involved in the project.

"One of our concerns is dependence on foreign oil and the U.S. balance of payments," explained William Knopka, the director of research for Goodyear. "One of the driving forces behind this is lessening dependence on other imports."

Next week an additional 30 acres of land south of here near Casa Grande, Ariz., will be planted with the guayule (pronounced why-oo-lee) seedlings.

The plantings are designed to produce seeds to be used in the next project phase -- a major planting in 1981 on private and Indian lands.

By the end of the decade, officials hope the plantings will cover more than 500 acres between Phoenix and Tucson.

"The commercialization of guayule undoubtedly will have a major impact not only on Arizona but on the whole nation," ASU Agricultural Division Director Richard R. Chalquest said earlier this month when the project was unveiled. "We are talking about developing a whole new industry in this country."

Later plans call for construction of a large processing plant which will extract latex from the guayule bush and produce baled rubber to be shipped to manufacturing points.

Knopka said the rubber produced from the shrub "can be cost-competitive" with synthetic and other natural rubber if properly cultivated.

Only about 20 percent of the plant contains rubber, he added. Goodyear hopes to burn the remaining 80 percent of the shrub as fuel to power the processing plant.

Goodyear has used sample quantities of guayule rubber to make tires for earth movers, autos and aircraft. Tests show its structure is similar to conventional tree-grown rubber, and that the tires are equal in performance to the company's F32 winter tires.

All natural rubber used in the United States now is imported, mostly from Southeast Asia. Goodyear officials said more than $900 million was spent to import rubber in 1979 -- making it the second-costliest import behind foreign oil.