In 1922, he tied for 4-5th in Innsbruck (Ernst Grünfeld and Rudolf Spielmann won).
The event was won by (Hermanis Matisons and Savielly Tartakower.
In 1932, Hans Müller won the European Correspondence Chess Championship (IFSB) ahead of Eduard Dyckhoff.
In 1935, he tied for 3rd-5th in Vienna (18th Trebitsch; Lajos Steiner and Eliskases won).
In 1937/38, he tied for 3rd-5th in Vienna (20th Trebitsch; Lajos Steiner won).
Hans Müller played for Austria five times in the Chess Olympiads and once in unofficial at Munich 1936.
The event was won by Paul Felix Schmidt and Klaus Junge.
In July 1942, he tied for 2nd-3rd, behind Ludwig Rellstab, in Bad Oeynhausen (9th GER-ch).
In 1944, he won in Posen (Reichsmeisterschaft «Kraft durch Freude»).
After World War II, Müller played in several Austrian championships since 1947 till 1960.
In 1957, he tied for 7-8th in San Benedetto del Tronto (Gedeon Barcza won).
Hans Müller played for Austria in friendly matches against Czechoslovakia (1949), Italy (1951, 1952) and the Soviet Union (1953).