The linear two-dimensional steady potential flow around a body moving at a constant depth below the surface of a liquid is computed by means of a composite grid method. A composite grid in the sense of the paper consists of exactly two grids, namely a curvilinear grid in the vicinity of the body and an overlapping Cartesian mesh for the discretization of the far field region. Boundary conditions at the far field are constructed from eigenfunction expansions of the solution. Second order accurate finite differences are used for the discretization of the equation. Numerical examples are given.