This study aimed to determine how radiation attenuation would change when the thickness, density, and compressive strength of clay bricks, modified with partial replacement of clay by fly ash, iron slag, and wood ash. To conduct this investigation, four distinct types of bricks—normal, fly ash-, iron slag-, and wood ash-incorporated bricks were prepared by replacing clay content with their variable percentages. Additionally, models for predicting the radiation-shielding ability of bricks were created using gene expression programming (GEP) and artificial neural networks (ANN). The addition of iron slag improved the density and compressive strength of bricks, thus increasing shielding capability against gamma radiation. In contrast, fly ash and wood ash decreased the density and compressive strength of burnt clay bricks, leading to low radiation shielding capability. Concerning the performance of the Artificial Intelligence models, the root mean square error (RMSE) was determined as 0.1166 and 0.1876 nC for the training and validation data of ANN, respectively. The training set values for the GEP model manifested an RMSE equal to 0.2949 nC, whereas the validation data produced RMSE = 0.3507 nC. According to the statistical analysis, the generated models showed strong concordance between experimental and projected findings. The ANN model, in contrast, outperformed the GEP model in terms of accuracy, producing the lowest values of RMSE. Moreover, the variables contributing towards shielding characteristics of bricks were studied using parametric and sensitivity analyses, which showed that the thickness and density of bricks are the most influential parameters. In addition, the mathematical equation generated from the GEP model denotes its significance such that it can be used to estimate the radiation shielding of burnt clay bricks in the future with ease.