The possibility of improving the convergence of Molodensky’s series is considered. Then new formulas are derived for the solution of the geodetic boundary value problem. One of them presents an expression for the boundary condition which involves a linear combination of Stokes’ constants and surface gravity anomalies. This differs from the usually used relation by the appearance of additional terms dependent on second order terns with respect to the elevations of the earth’s surface. The formulas are derived for Stokes’ constants and the anomalous potential in terms of surface anomalies. As compared to the Taylor’s series of Molodensky, they are presented in the form of surface harmonic series. Due regard is made to the earth’s oblateness, in addition to the terrain topography.