Solutions of a linear hydrodynamic equation of motion with linear boundary conditions are obtained to describe the horizontal current, as a function of depth and time, determined by a given history of the wind force and pressure gradient up to that time, at a fixed point in the horizontal plane in well-mixed water of finite depth. The bottom friction is assumed to be proportional to the bottom current, with zero bottom current and zero bottom friction considered as limiting cases. The general solution is established as an eigenfunction expansion when the eddy viscosity is given as a positive function of depth. Eplicit formulas are worked out for viscosity functions that are constant, exponential, or varying as a power of the height from somewhere below the bottom or above the top of the water. (Copyright (c) 1980 American Meteorological Society.)