The dynamic anti-plane problem of trifurcation of a semi-infinite crac
k due to incidence of two linearly varying plane SH-waves with non-par
allel wave fronts in an infinite elastic medium has been considered. T
he semi-infinite crack is assumed to trifurcate when the plane waves i
ntersect the crack tip. The problem has been solved using the self-sim
ilar technique, which is based on the observation that certain field v
ariables show dynamic similarities. The results include the expression
s for shear stress in the planes of the cracks and the stress intensit
y factors at the crack tips. Numerical calculations have been carried
out to show the variations of stress intensity factors at the crack ti
ps with the angle of skew for different values of the crack tip veloci
ty and angle of incidence.