Equations of subsurface flow of water, the Richards equation and the Boussinesq equation, have no known exact analytical solutions. Approximate analytical solutions to these equations have been developed under linearizing simplifications. In the first part of the dissertation two commonly used linear methods of computation of groundwater flow are investigated. The equation considered includes a recharge term and slope of an impervious bed. A new method of computation with improved accuracy has been developed. The second part of the dissertation deals with vertical, unsaturated flow of water in a homogeneous soil column of finite length with arbitrary initial conditions. The boundary conditions considered at the soil surface correspond to pre-ponding and post-ponding infiltration. / Ph. D.