He played for Colombia in six Chess Olympiads: 1954, 1956, 1958, 1964, 1970, and 1972. In 1958, he tied for 2nd-3rd with William Lombardy, behind Oscar Panno, in Bogotá. In 1962, he placed 22nd at the Stockholm Interzonal, defeating both Efim Geller and Viktor Korchnoi in individual games.
In 1969, he tied for 1st with Boris De Greiff in Bogotá.
He was awarded the International Master (IM) title in 1957.
Cuéllar won the Colombian championship nine times: in 1941, 1946, 1953, 1955, 1956, 1957, 1959, 1961, and 1971. He won individual silver medal at first board (+12 –2 =4) in the 16th Olympiad at Tel Aviv 1964. In 1952, he tied for 3rd-4th in March del Plata (Julio Bolbochán and Héctor Rossetto won). In 1953, he took 5th in March del Plata (Svetozar Gligorić won). In 1957, he took 7th in March del Plata (Paul Keres won). In 1961, Cuéllar won in Caracas (zonal). In 1966, he took 7th in Havana (Eleazar Jiménez won). In 1967, he tied for 19-20th in Sousse (interzonal. Bent Larsen won). In 1970, he took 7th in Bogotá (Henrique Mecking won). In 1970, he took 14th in Caracas (Lubomir Kavalek won). In 1973, he took 18th in Leningrad (interzonal. Anatoly Karpov and Viktor Korchnoi won). In 1980, he tied for 4-5th in Bogotá (Joaquin Gutierrez won).
