Melanie Smith, last year's winner of the President's Cup Grand Prix, heads the list of riders for the 1982 edition of The Washington International Horse Show beginning today at Capital Centre.

Smith, 33, of Litchfield, Conn., rode Windrush Farm's Calypso to victory here last year and won the final of the World Cup in Gothenburg, Sweden, this spring.

She will be joined on the United States Equestrian Team by Donald Cheska, 22, of Waukesha, Wis., a recent winner in Baltimore; Norman Dello Joio, 26, of South Salem, N.Y., and Katie Monahan, 27, of Upperville, Va.

Riders from 34 states, the District of Columbia and seven foreign countries will compete for more than $160,000 in prize money -- up $10,000 from 1981 -- during the eight-day event.

Tonight's opening performance begins at 5 with carriage driving competition, terrier races and international jumping scheduled. There also will be an exhibition by the Black Stallion.

Although not listed on the U.S. team, Rodney Jenkins, three-time winner of the President's Cup, is scheduled to ride as an individual. Jenkins, 37, of Gordonsville, Va., is the all-time leading money winner in U.S. grand prix competition.

During the 1970s, Jenkins and his mount Idle Dice dominated U.S. show jumping. The 20-year-old brown gelding is one of three horses Jenkins has entered in the international jumping events.

The Washington International is the first of the final three major jumping events on the year-long circuit that begins in Florida in February and ends in November in Toronto.

It is the first stop of what is known as the "indoor circuit," with shows in New York and Toronto following. Washington's also is the only show on the indoor circuit in which the international riders compete directly against the national riders, both amateur and professional.

For the team members only, there is Tuesday evening's Nation's Cup class, the first of three held during the indoor circuit. This event can be held only at certain shows, such as Washington's, where an international rating has been given by the Federation International Equestre.

In order to acheive this status, the event must finance the travel and living expenses of the foreign competitors. Washington shares the air fare and travel estimated at $240,000 for both horses and riders with the New York and Toronto shows.

Visiting this year will be France, Switzerland and Canada. Frederick Cottier, 28, Patrick Caron, 32, and Michel Robert, 34, make up the French team. Switzerland will be represented by Markus Fuchs, 27, Thomas Fuchs, 25, Walter Gabathuler, 28, and Philippe Guerdat, 30.

Mac Cone, 29, of Cheltenham, Ontario, a former member of the U.S. team, will represent Canada along with Terrance Millar, 37, Kim Kirton, 22, and Danny Foster, 30. Individual riders from Venezuela, Japan, Ecuador and Great Britain will also ride.