Tsintsadze studied the cello until 1942 with E.N. Kapelniski in Tbilisi at the Gymnasium of Music. He furthered his studies of the cello at the Conservatory of Tblisi with K. Minjar. From the years 1945 to 1953 he went to the Moscow Conservatory to study the cello with Semyon Matveyevich Kozolupov and composition with Semyon Semyonovich Bogatyryov.
He began his musical career in the 1940s as the cellist in the Georgian State String Quartet. His first composition, based on Georgian folksongs and being a collection of miniatures for string quartet, was an immediate success. He also wrote several operas, ballets, symphonies and concertos, but it was his compositions for string quartet which came to take pride of place amongst his works and which made a notable contribution to Georgian music. Tsintsadze's compositions are based on the traditional forms as well as styles and characteristics used by composers such as Shostakovich and Shebalin. Georgian folklore is ever present in his music.
Sulkhan Tsintsadze was one of Georgia's leading composers. He was awarded the People's Artist of Georgia (1961) and People's Artist of the USSR (1987) titles and was a holder of the USSR Stalin Prize (1950), Shota Rustaveli Prize (1981), Z. Paliashvili Prize (1977).
- Three Miniatures for string quartet (1945) Duration: 6'
- String Quartet No. 1 (1947) 28'
- Cello Concerto No. 1 (1947) 20'
- Violin Concerto No. 1 (1947)
- Two Pieces for viola and piano (1948) 7'
- Khorumi, Georgian Dance
- String Quartet No. 2 (1948) 28'
- Piano Concerto No. 1 after Georgian Themes (1949) 20'
- Fantasy for piano and orchestra; revision of Piano Concerto No. 1 after Georgian Themes (1949)
- Five Pieces on Folk Themes for cello and piano (1950) Duration: 10'
- Villain's Song on a Carriage
- Tchonguri (Chonguri)
- Dance Tune
- String Quartet No. 3 (1951) 30'
- Suite for string quartet (1951) 15'
- Symphony No. 1 (1952) 28'
- The Golden Fleece, opera after the saga of the argonauts (1953); libretto by Ira Gelovani. 130'
- Fantasy for piano and orchestra (1954) Duration: 20'
- The Treasure of the Blue Mountain, children's ballet in three acts (1954); libretto by Ira Gelovani. 100'
- Suite from the ballet "The Treasure of the Blue Mountain" (1954)
- Music to the Film "The Dragon-Fly" (1954)
- Suite from the music to the Film "The Dragon-Fly" (1954) 18'
- String Quartet No. 4 (1955) 30'
- Suite No. 3 for string quartet (1955) 15'
- Farewell-Song, cantata after Yelena Drushima for solo voices, chorus and orchestra (1956)
- Demon, ballet in three acts after Michail Lermontov (1958); libretto by V. Tsabukiani; first performance in 1961 in Tblisi. 130'
- Suite from the ballet "Demon" (1958) 30'
- Seventeen Miniatures for string quartet (1961) 40'
- String Quartet No. 5 (1962) 32'
- Symphony No. 2 (1963)
- The Spider's Web, operetta (1963)
- Cello Concerto No. 2 (1964) 36'
- Georgian Melodies for cello and piano (1967) 26'
- String Quartet No. 6 (1967) 18'30"
- Singing in the Forest, operetta (1967); libretto by Lewan Tsubabrya
- Violin Concerto No. 2 (1967) 28'
- Piano Concerto No. 2 (1968)
- Symphony No. 3 (1969) 25'
- Immortality, oratorio after M. Pozshivili for mezzo-soprano, chorus and orchestra (1969) 34'
- String Quartet No. 7 "To the Memory of Bela Bartok" (1970)
- Twenty-Four Preludes for piano (1971) 45'
- The Hermit, opera in one act after Ilja Tshavtshavadze (1972); libretto by Pjotr Grusinsky; first performance in 1972 in Tblisi. 45'
- Antique Sketches, ballet in one act after Georgi Aleksidze (1973)
- Cello Concerto No. 3 (1973)
- Five Romances after Pjotr Grusinsky for high voice and piano (1974)
- String Quartet No. 8 (1974) 18'
- Schweyk against Frans Joseph, operetta (1974)
- The Milkstreet, cantata after Pjotr Grusinsky for soprano, chorus and orchestra (1975) 20'
- Suite from the ballet Antique Sketches (1975)
- Dali and the Hunters, ballet (1975); libretto by Georgi Aleksidze
- Sonata for cello solo (1975)
- Concertino for cello and orchestra (1976) 30'
- Fantasy for string quartet and orchestra (1977)
- String Quartet No. 9 (1978); dedicated to the memory of Dmitri Shostakovich
- Twelve Miniatures for string quartet (1978) 30'
- Twenty-Four Preludes for violin, celesta, piano, bells and chamber orchestra (1978)
- Twelve Children Songs after Chuta Berulav for voice and piano (1979)
- Twelve Children's Pieces for piano (1979)
- Symphony No. 4 (1979)
- Twenty-Four Preludes for cello and piano (1980)
- String Quartet No. 10 "Polyphonic" (1984)
- String Quartet No. 11 (1986)
- Eight Miniatures on Georgian Folk Tunes for string quartet (1988)
- Ballad of a Soldier, Requiem (1988)
- Fantasy after themes from Dolidze's opera "Keto and Kote" for violin and strings (1989)
- Five Miniatures on Jewish Folk Tunes for string quartet (1990)
- Fantasy on Themes from Gershwin's "Porgy and Bess" for violin and chamber orchestra (1991)
- String Quartet No. 12 (1991)
- And furthermore:
- Pieces for chamber orchestra
- Incidental Music
- Film Music
His major works are:
- 12 string quartets and miniatures for quartet (1947-1991)
- Two operas ("Gandegili" 1972)
- Five ballets ("Demon" 1961, "Rivares" 1982)
- Five symphonies (1952-1985)
- 24 preludes for cello and orchestra (1980) and violin and orchestra (1987)
- 2 concertos for piano and orchestra
- Concertino for cello and chamber orchestra
- 2 concertos for cello and orchestra
- 2 concertos for violin and orchestra
- 3 operettas ("ablabuda" - 1960, "simgera tkeshi" - 1967, "shveiki" - 1976)
- Five Pieces for cello and piano
- A lot of film-music