Abstract: In the paper the authors have studied the influence of the geodetic singularity on geodesy and the structure of the gravity field near the singular point, exposed the nature of the singularity, and drawn the following conclusions1 reference Isolated geodetic singular points are removable; reference2 Under the condition that Gauss curvature of equipotential surface is non negative and geodetic torsion of meridian vanishes. If there exist geodetic singular points on the equipotential surface of the earth's gravity field, their number is finite and they are isolated.