By increasing the usage of radiation in all aspects of lives, the human body is becoming more exposed to ionising radiation. The purpose of this study is to find the optimal radiation shielding materials to protect humans from the radiation hazards of radiation. Some elements and compounds such as Ag, Bi, Pb, W, BaSO4 were chosen on the basis of their attenuation coefficients and other characteristics to produce optimised radiation shielding compounds. Multi-objective non-dominated sorting genetic algorithm-II was used to optimise the weight fraction of the elements in compounds based on the dose equivalent rate, shield weight and cost. Consequently, sets of suitable compounds were obtained depending on various applications for energy 0.06 and 0.15 MeV. In addition, optimised lead free compounds were obtained. The results presented in a series of graphs should enable radiation shield designers to choose an appropriate combination according to their requirements.