Abstract: Starting from the equations of Solid Mechanics, one type of inverse problem in the form of the defferential equation is proposed and defined as the inverse problem of Dynamic Geodesy. The properties and solutions of the inverse problem are investigated by the finite element method and regularization method, and a regularization method for inversion of dynamic geodetic data is given. Finally, the application of the inversion method in the research of the non-uniform rupture of earthquakes is discussed, and the pattern of the coseismic non-uniform rupture of the Tangshan earthquake of 1976 is determined by inversion of geodetic data.