Abstract Considering the fault as a crack in the infinite elastic space, the field of displacement and stress due to forces acting on the lateral surfaces of the crack are obtained. The use of Fourier and Laplace transform methods yield dual integral equations. The solution to these dual integral equations and the formal expressions for the displacements and stresses in terms of integrals are obtained. The forces acting on the lateral surfaces of the crack are assumed to have the following three forms: (a) compressive stress perpendicular to the surfaces of the crack; (b) shear stress along the dip-direction of the crack; (c) shear stress along the strike-direction of the crack. Numerical results are calculated for various values of frequency and Poisson's ratios.