A method for analysis of internal cracks in plates and shells is presented. The formulation assumes that the surface of the internal crack is constructed from two semi-ellipses of different depths; thus, the geometry of the crack is defined by three elliptic half axes. The potential energy of the body with the crack is calculated using a finite element formulation based on 20-node isoparameteric solid elements. High numerical efficiency of the analyses of different crack shapes is obtained by means of the substructure concept. Least square functional fitting is used for finding the energy release rates associated with incremental extensions of the ellipic half axes. The growth of the crack during load cycling is found by integrating three coupled crack growth equations as an initial-value problem. The geometry of the growing crack is visualized by plots of the crack periphery for prescribed numbers of load cycles.