Non-seismic-designed reinforced concrete (RC) pier walls often include lap splices in potential plastic hinge regions. This study develops an analytical model to capture the post-yield load–deformation response of lap-spliced RC pier walls subjected to earthquake loading. The parameters of the model were calibrated using experimental results, and linear regression was conducted to propose predictive equations for these parameters. The accuracy of the model was validated by comparing it to the load–deformation responses of specimens not included in the calibration database. Subsequently, the developed model was applied to probabilistic bridge models supported by RC pier walls. A multi-parameter seismic demand model was constructed, taking into account geometric, material, and structural uncertainties, using Lasso regression. This model achieved R² values of 0.73 for in-plane loading and 0.75 for out-of-plane loading. The improvements in performance metrics and the results of the sensitivity analysis emphasize the need to develop a multi-parameter seismic demand model to ensure more reliable seismic demand predictions.