ON SATURDAY, continuing with its Andrei Tarkovsky film series, the National Gallery of Art will screen Andrei Rublev, Tarkovski's black-and-white study of the 15th-century Russian artist, at the East Building auditorium. Shows are free, Saturday at 1:30 and Sunday at 6.

Steven York and Foster Wiley, who made Vietnam Memorial, about the five-day National Salute to Vietnam Veterans in Washington in 1982, will present their 55-minute film Tuesday at the American Film Institute. "Vietnam" is preceded by The Secret Agent, Jacki Och's 57-minute film about chemical warfare and the effects of Agent Orange on Vietnam vets. Admission is $4.50, $3.50 for members. The show starts at 8:45.

The Smithsonian Resident Associates will sponsor a Canadian film series. First up is Giles Walker's 90 Days (1987), described succinctly as "One comedy, two plots, involving a mail-order bride and a sperm donor." (shown Monday, December 7); followed by Pouvoir Intime (Blind Trust) a 1986 thriller (in French with subtitles) by Yves Simoneau. Then, December 14, it's Anne Wheeler's Loyalties (1986). Price for the full series is $14 (for members) and $18 (nonmembers). Individual screenings are $5 and $6.50. All shows are at 7:30 at the Carmichael Auditorium of the American History Building. Call 257-4090.

In the free zone: Tuesday at noon, The Stone Carvers, the Oscar-winning short by local filmmakers Paul Wagner and Majorie Hunt, can be seen at the National Geographic Society, 1600 M St.; in the Gilbert H. Grosvenor Auditorium. It's shown with Holy Stone, a short about marble quarry workers in Italy. Call 857-7133 . . . Also Tuesday (7:30), at the Library of Congress' Mary Pickford Theater, it's Steve Rash's warm The Buddy Holly Story, with Gary Busey. Call 287-5677 for reservations . . . Thursday at 1, at the Organization of American States' General Secretariat Building, classroom B (room 640-J, sixth floor) 1889 F St. NW, see the 30-minute shorts Japan, An Overview and A Cultural Journey into Japan. Call 458-3673 . . . Also Thursday (11 a.m. and 12:15), the Renwick Gallery will show Hopi: The Songs of the Fourth World, about Hopi culture. It's in conjunction with the Renwick's "Lost and Found" exhibition.