The object of this article is to study the numerical method for solving two-dimensional transient response of a strip with a central crack subjected to shear stresses acting on the surface of the strip. The characteristic method for two-space variables is employed to solve the problem. The method employs the explicit finite-difference approximations with second order accuracy based on the integration of the characteristic equations along bicharacteristics. Numerical calculations are carried out for the shear stress wave propagations and the stress intensity factor K_<III>, and the results are shown in figures.