In the last year a new formulation of Molodensky’s problem has been given, in which the gravity vector \(\vec g\) has been considered as the independent variable of the problem, while the position vector \(\vec x\) is the dependent. This new approach has the great advantage to transform the problem of Molodensky which is of free boundary type, into a fixed boundary problem for a non linear differential equations. In this paper the first results of the study of the new approach are summarized, without going into many mathematical details. The problem of Molodensky for the rotating earth is also discussed.