This paper is devoted to the study of dynamical problems for moving cracks in materials with initial stresses, taking into account the author's previous publications on this subject. Stresses and displacements in linearized theory are represented through analytic functions of complex variables in dynamical problems. Exact solutions of dynamical problems are obtained for moving cracks in materials with initial stresses in the case of transverse shear (Mode II) and longitudinal shear (Mode III); these results are obtained for general cases of equal and unequal roots of the basic equation. New mechanical effects are analyzed in the dynamical problems under consideration. The results are obtained for compressible and incompressible bodies with elastic potentials of arbitrary structure.