The boundary collocation method is used to obtain the torsional rigidity and Mode III stress intensity factor of a thick-walled cylinder with an external radial crack. When the internal radius of the cylinder is very small, the results agree well with those obtained previously from other methods for an edge crack in a solid cylindrical bar. The present method is shown to be expedient when applied to obtain results for different ratios of the internal and external radii of the cracked cylinder.