In this study an axially symmetric conical crack problem in semi-infinite media is considered. Stress-free boundary conditions are satisfied at the boundary of the half-space. By using Papkovich-Neuber functions and Hankel transform techniques the problem is reduced to a system of two singular integral equations which are then solved numerically. The numerical examples are given for a constant pressure and constant shear stress on the crack surface separately. The stress intensity factors are evaluated and presented for various crack geometries and Poisson's ratios. © 1986 Martinus Nijhoff Publishers.