Young Radomir attended the "Vuk Karadžić" primary school and the Second Men's Gymnasium in Belgrade, from which he graduated in 1944. In 1946, he enrolled in the Faculty of Technology and Metallurgy of the University of Belgrade, graduating in 1950. He earned his doctorate degree in 1964, became an associate professor in 1968, and a full professor at the Faculty four years later. In 1980, Professor Šaper was appointed Vice-Dean of the Faculty and worked there until his retirement in 1991.