A numerical model is presented to analyze a two-dimensional, time-dependent heat transfer and flow process in a melting, heterogeneous snow cover with the underlying soil layer that is permeable and initially frozen. The model considers flow fingering phenomena due to variation of permeability in layered snow. A unit block ofsnowpack is modeled and divided into a heterogeneous domain with specified number of snow layers and a water-fingering domain with initially uniform properties, in addition to coupling with a formulation of infiltration in the frozen soil. Typical results of snow depth, wetting front location, snow water equivalent, basal ice thickness, and soil infiltration show good agreement with experimental data under field conditions. A parametric study is performed to investigate the sensitivity of several properties and parameters in boundary conditions.