The problem of determining the transient stress distribution in an infinite orthotropic plate weakened by two coplanar Griffith cracks is considered. An internal pressure is applied suddenly to the surfaces of the cracks. Application of the Fourier and Laplace transforms reduces the problem to the solution of a pair of dual integral equations in the Laplace transform plane. To solve these equations, the crack surface displacement is expanded in a series of functions which are zero outside of the cracks. The unknown coefficients accompanying in that series are solved with the aid of the Schmidt method. The stress intensity factors defined in the Laplace transform plane are inverted numerically in the physical plane. Numerical calculations are carried out for Boron-Epoxy composite materials. ************************************