One of the most important applications of gravity surveys in regional geophysical studies is determining the depth to basement. Conventional methods of solving this problem are based on the spectrum and/or Euler deconvolution analysis of the gravity field and on parameterization of the earth’s subsurface into prismatic cells. We have developed a new method of solving this problem based on 3D Cauchy-type integral representation of the potential fields. Traditionally, potential fields have been calculated using volume integrals over the domains occupied by anomalous masses subdivided into prismatic cells. This discretization can be computationally expensive, especially in a 3D case. The technique of Cauchy-type integrals made it possible to represent the gravity field and its gradients as surface integrals. In this approach, only the density contrast surface between sediment and basement needed to be discretized for the calculation of gravity field. This was especially significant in the modeling and inversion of gravity data for determining the depth to the basement. Another important result was developing a novel method of inversion of gravity data to recover the depth to basement, based on the 3D Cauchy-type integral representation. Our numerical studies determined that the new method is much faster than conventional volume discretization method to compute the gravity response. Our synthetic model studies also showed that the developed inversion algorithm based on Cauchy-type integral is capable of recovering the geometry and depth of the sedimentary basin effectively with a complex density profile in the vertical direction.