Movement of snowmelt water through a thin saturated layer at the infiltrating base of a snowpack is modelled by applying the kinematic wave theory. Analytical solutions are obtained for flow depth, velocity and discharge assuming that the rate of input to the saturated layer due to vertical percolation is constant. This assumption results in a linear rise and recession of the snowmelt hydrograph. The solutions are extended to the case of time-varying input. An explicit consideration of infiltration leads to a free boundary problem.