The timing and magnitude of snowmelt discharge and subsequent runoff are controlled by both matrix and preferential flows of water through snowpacks. Matrix flow can be estimated using the Richards equation, and recently, preferential flow in snowpacks has been represented in 2D and 3D models. A challenge for representing preferential flow through porous media in 2D or 3D is capillary pressure overshoot in 1D. Soil studies have developed sophisticated and largely realistic approaches to represent capillary pressure overshoot, but it has not been addressed in snowpack water flow models. Here a 1D nonequilibrium Richards equation model is implemented with dynamic capillary pressure and is combined with a new concept of entrapment of liquid water within the pore space. This new model well represented capillary pressure overshoot, as estimated by published capillary pressure measurements in snow samples of various grain sizes under different rates of liquid water infiltration. Three model parameters were calibrated, and their impacts on model outputs were evaluated. This improvement is a substantial step toward better understanding and simulating physical processes occurring while liquid water percolates an initially dry snowpack.