A computer model using the alternating direction implicit (ADI) finite difference method to study two-dimensional coupled soil heat and water flow with a partial surface mulch cover is developed. A new, simplified computational procedure, which has only tridiagonal matrix problems, for the ADI method is introduced. The model uses a soil surface energy balance equation to determine soil surface boundary conditions for both heat and water flow. The inputs required for the computer simulations are weather data, soil thermal and hydraulic properties, and mulch data. Numerical experiments are performed to examine the effects of soil type, mulch width, and weather conditions on soil heat and water movement. For continuous evaporation and drainage, 10-day simulations were performed for each combination of clay, loam, and sand soil and fractions of mulch cover of 0, 0.5, 0.8, and 1.0 of the row interval width. For repetitive evaporation and infiltration, 15-day simulations were performed. The mulch cover greatly reduces evaporation loss and the amplitude of daily soil temperature, water content, and pressure head variations. Large spatial variations in temperature and soil water content are predicted near the interface of mulch and bare soil surface. The soil hydraulic properties have important roles in controlling soil surface water content. The present model reasonably describes the soil thermal and hydrologic environments and thus can be applied successfully in soil science and groundwater hydrology and can be extended to related disciplines.