Concrete is an economical and efficient material for attenuating radiation. The potential of concrete in attenuating radiation is attributed to its density, which in turn depends on the mix design of concrete. This paper presents the findings of a study conducted to evaluate the radiation attenuation with varying water-cement ratio (w/c), thickness, density, and compressive strength of concrete. Three different types of concrete, i.e., normal concrete, barite, and magnetite containing concrete, were prepared to investigate this study. The radiation attenuation was calculated by studying the dose absorbed by the concrete and the linear attenuation coefficient. Additionally, artificial neural network (ANN) and gene expression programming (GEP) models were developed for predicting the radiation shielding capacity of concrete. A correlation coefficient (R), mean absolute error (MAE), and root mean square error (RMSE) were calculated as 0.999, 1.474 mGy, 2.154 mGy and 0.994, 5.07 mGy, 5.772 mGy for the training and validation sets of the ANN model, respectively. Similarly, for the GEP model, these values were recorded as 0.981, 13.17 mGy, and 20.20 mGy for the training set, whereas the validation data yielded R = 0.985, MAE = 12.2 mGy, and RMSE = 14.96 mGy. The statistical evaluation reflects that the developed models manifested close agreement between experimental and predicted results. In comparison, the ANN model surpassed the accuracy of the GEP models, yielding the highest R and the lowest MAE and RMSE. The parametric and sensitivity analysis revealed the thickness and density of concrete as the most influential parameters in contributing towards radiation shielding. The mathematical equation derived from the GEP models signifies its importance such that the equation can be easily used for future prediction of radiation shielding of high-density concrete.