The majority of radiation fields are synthesis of various radiation types. The most significant radiations include primary gamma rays, secondary gamma rays, thermal neutrons, and fast neutrons. These kinds of radiation are intended to be attenuated by thermo composite shielding materials. Modern medical cyclotrons that generate significant quantities of short-lived radioisotopes must be operated safely which requires effective radiation shielding. For the shielding design, a precise cost-benefit analysis is needed. For functions involving several variables, like the medical cyclotron shielding design's cost-benefit analysis, the traditional optimization method is complicated. Hence the cost-benefit analysis of a medical cyclotron has been formulated and solved using interval programming. The main objective of this paper is to find the thickness of the concrete shielding wall to provide the maximum radiation safety at the lowest operational and material costs. We formulate an interval shielding cost optimization problem of medical cyclotron. In this optimization problem the interval parameters (parameter is a constant may be vary) will be in both objective functions and constraints. We demonstrate that an interval optimization approach is a suitable method for the radiological shielding design of concrete vaults holding cyclotron targets to generate medicinal radioisotopes.