A box culvert, buried at shallow depths beneath roadways, may experience deflections caused by the dynamic impact of traffic loading and the vertical pressure exerted by the soil fill. A computational model commonly employed used to various engineering issues, including those in geotechnical applications, is the beam-on-elastic-foundation model. In this context, the Moment Distribution Method (MDM) must be applied to account for the elastic foundation. To achieve this, the internal forces acting on the ends of both exterior and interior walls are transferred to the beam-like bottom slab of the culvert, which rests on an elastic soil bed. Subsequently, the secondary internal forces are determined by refining the structural parameters, taking into account the characteristics of the elastic soil bed. This study presents the development and application of an Artificial Neural Network (ANN) model to predict the shear capacity of box culverts on elastic soil under traffic loading conditions. The proposed model is trained and validated using a comprehensive database of beam on elastic foundation solutions. The input parameters include the geometrical and mechanical properties of the culvert and the soil, as well as the loading conditions. The results of the ANN model show R2 values of 0.9633 and 0.9581 for the training and testing sets, respectively, indicating the model's excellent accuracy. These findings suggest that the ANN model can reliably predict the shear capacity of culverts.