Desiccation-induced cracking in clay soils significantly affects the structural performance and durability of geotechnical systems. This study presents a data-driven approach to predict the Crack and Shrinkage Intensity Factor (CSIF), a comprehensive index quantifying both crack formation and shrinkage behavior in drying soils. A database of 100 controlled desiccation tests was developed using five clay mixtures with varying plasticity indices, which were subjected to a range of drying rates, soil thicknesses and initial conditions. Four predictive models—Multiple Linear Regression (MLR), Classification and Regression Random Forest (CRRF), Artificial Neural Network (ANN) and Genetic Programming (GP)—were evaluated. The ANN model using Bayesian Regularization demonstrated superior performance (R = 0.99, MAE = 5.44), followed by CRRF and symbolic GP equations. Sensitivity analysis identified drying rate and soil thickness as the most influential parameters, while initial moisture content and ambient conditions were found to be redundant when the drying rate was included. This study not only advances the predictive modeling of desiccation cracking but also introduces interpretable equations for practical engineering uses. The developed models offer valuable tools for crack risk assessment in clay liners, soil covers and expansive soil foundations.