John Crisp completed his Bachelor of Engineering with honours in Civil Engineering at the University of Adelaide in 1950. He then went on to complete a fellowship diploma in civil engineering at the South Australian School of Mines in 1951. From 1951-53 Crisp worked as an attached scientist (Australian Department of Supply Trainee Officer) for the Royal Aircraft Establishment in England. He went on to work for Vickers-Armstrong Aeroelastic Group Technical Office also in England, again as an attached scientist.
Crisp then returned to the University of Adelaide, where he completed his Masters of Engineering, graduating in 1956. In May 1957 he took up a position as a research engineer at Massachusetts Institute of Technology. After two years he left Massachusetts to take up a position at the Polytechnic Institute of Brooklyn in the Applied Mechanics Group. There he was a research assistant professor until June 1960 when he was promoted to research associate professor in Applied Mechanics. Crisp was one of the first to apply for the lectureships that were advertised in Engineering at Monash University in 1960. He was offered the position of senior lecturer in engineering in September 1960.
In 1962 he applied for the position of Chair of Structures in Engineering, however was unsuccessful. When the Departments were formed, Crisp became part of the Department of Applied Mechanics. When Dean and Head of the Department Ken Hunt went overseas during the second half of 1964, Crisp became temporary Head of Department. In December of that same year, he was promoted from Senior Lecturer to Reader. The very next year he became Associate Professor in Applied Mechanics. In 1967 he was made Professor of Engineering Dynamics.
In November 1981, Crisp was elected to the Fellowship of the Australian Academy of Technological Sciences. A year later in 1982, he was made a Member of the Order of Australia.