Ticket applications for the 1984 Olympic Games in Los Angeles will be available beginning today at 3,700 locations throughout the country, including 3,300 Sears Roebuck and Co. stores and catalogue outlets.

More than 8 million tickets are available for the Games, the Los Angeles Olympic Organizing Committee said. About 70 percent, or 5.6 million, can be purchased through the mail order forms available at the Sears outlets, and at 198 Manufacturers Hanover Trust branches in New York City and 204 First Interstate Bank branches in Southern California.

The remaining 30 percent of the Olympic tickets will be set aside for Olympic officials, athletes and coaches, news media, and for people living outside the United States and by Olympic sponsors and other supporters.

Ranging in price from $3 to $95, the tickets for sporting events will be distributed on a first-in, first-served basis except for those events that are oversubscribed by Aug. 15. A computerized random drawing will be held for those tickets.

Tickets for the Olympic opening and closing ceremonies in the Los Angeles Coliseum will cost $50, $100 and $200. The average ticket price will be $17 and almost half the tickets will cost less than $10 apiece.

There will be 370 separate sports events in 21 Olympic sports and two demonstration sports (baseball and tennis) during the Los Angeles Games, which will run from July 28 through Aug. 12 of 1984. Thirty events, including the opening and closing ceremonies and finals for basketball, gymnastics, swimming, diving, boxing and volleyball, have been designated premium events and tickets will be limited to two per person.

Forty-five other events, including basketball quarterfinals and semifinals and selected sessions of the track and field competitions will be semipremium events and the tickets will be limited to four per person.

There will be more than 400,000 tickets available for first-round Olympic soccer competition on the East Coast, at the Navy-Marine Corps Memorial Stadium in Annapolis and at Harvard Stadium in Cambridge, Mass.

In addition to purchasing tickets for single sporting events, Olympic sports fans may also purchase "season tickets" that will guarantee the same seat for every event in a particular sport. Prices for those tickets range from $1,000, $1,500 and $2,000 for basketball to $15, $35 and $50 for the six preliminary soccer matches in Annapolis and Cambridge.

The order forms are accompanied by a 32-page brochure describing the time, location and ticket price for each Olympic sports event and a pre-addressed envelope to LAOOC-1984 Ticket Orders, P.O. Box 60728, Los Angeles, Calif. 90060.

Tickets will be distributed next June, but purchasers will receive written notification that their orders have been received within 60 to 90 days beginning this fall. A check, money order or American Express, Master or Visa charge card number should accompany each order.

The LAOOC says it hopes to raise $90 million in ticket sales.