The dynamic anti-plane problem of extension of cracks due to the incid
ence of two linearly varying plane SH-waves with non-parallel wave fro
nts in an infinite elastic medium has been considered. The cracks are
assumed to appear at a point where the plane waves intersect. The prob
lem has been solved using a self-similar technique, which is based on
the observation that certain field variables show dynamic similarities
. The results include the expressions for shear stress in the planes o
f the cracks and the stress intensity factors at the crack tips.