Heinz Rutishauser's father died when he was 13 years old and his mother died three years later, so together with his younger brother and sister he went to live in their uncle's home. From 1936, Rutishauser studied mathematics at the ETH Zürich where he graduated in 1942. From 1942 to 1945 he was assistant of Walter Saxer at the ETH and from 1945 to 1948 a mathematics teacher in Glarisegg and Trogen. In 1948 he received his PhD from ETH with a well-received thesis on complex analysis.
From 1948 to 1949 Rutishauser was in the United States at the Universities of Harvard and Princeton in order to study the state of the art in computing. From 1949 to 1955 he was a research associate at the Institute for Applied Mathematics at ETH Zürich recently founded by Eduard Stiefel, where he worked together with Ambros Speiser on the development of the first Swiss computer ERMETH, and developed the programming language Superplan (1949–1951), the name being a reference to "Rechenplan" (i.e. computation plan), in Konrad Zuse's terminology designating a single Plankalkül-program. He contributed in particular in the field of compiler pioneering work and was eventually involved in defining the programming languages ALGOL 58 and ALGOL 60.
Among other contributions, he introduced a number of basic syntactic features to programming, notably the keyword for for a for loop, first as the German für in Superplan, next via its English translation "for" in ALGOL 58.
In 1951 Rutishauser became a lecturer (in German, a Privatdozent), and in 1955 he was appointed extraordinary professor and 1962 Associate Professor of Applied Mathematics at the ETH. In 1968 he became the head of the Group for Computer Science which later became the Computer Science Institute and ultimately in 1981 The Division of Computer Science at ETH Zürich.
At least since the 1950s Rutishauser suffered from heart problems. In 1964 he suffered a heart attack from which he recovered. He died on 10 November 1970 in his office from acute heart failure. After his untimely death, his wife Margaret took care of the publication of his posthumous works.
- Automatische Rechenplanfertigung. Habilitationsschrift ETHZ, 1951. (i.e. Automatic construction of computation plans, habilitation thesis)
- Automatische Rechenplanfertigung bei programmgesteuerten Rechenmaschinen. Basel: Birkhäuser, 1952.
- Some programming techniques for the ERMETH, JACM, 2(1), pp. 1–4, Januar 1955.
- Der Quotienten-Differenzen-Algorithmus. Basel: Birkhäuser, 1957.
- Vorlesungen über numerische Mathematik. Band I: Gleichungssysteme, Interpolation und Approximation. Martin Gutknecht (Hrsg.). Basel: Birkhäuser, 1976. ISBN 3-7643-0810-9.
- Vorlesungen über numerische Mathematik. Band II: Differentialgleichungen und Eigenwertprobleme. Martin Gutknecht (Hrsg.). Basel: Birkhäuser, 1976. ISBN 3-7643-0850-8.
- Heinz Rutishauser, Ambros Paul Speiser, Eduard Stiefel: Programmgesteuerte digitale Rechengeräte (elektronische Rechenmaschinen). Basel: Birkhäuser, 1951.
- Hans Rudolf Schwarz, Heinz Rutishauser, Eduard Stiefel: Numerik symmetrischer Matrizen. Stuttgart: Teubner, 1972, 2. Auflage, ISBN 3-519-12311-8.
- Numerische Prozeduren. Aus Nachlass und Lehre. Walter Gander (Hrsg.). Basel: Birkhäuser, Mai 1998, ISBN 3-7643-0874-5.