A method for interpretation of potential geophysical fields, based on a stable inversion algorithm, is proposed. The stability of the algorithm is provided by an original choice of the zero approximation model and stepwise solution of the inverse problem by a correctness set. The three-dimensional density distribution of local structures as grid functions is reconstructed by layer-wise anomalies of a spilt field. Examples of interpretation of the practical gravimetric data illustrating the efficiency of the method are given.