In this study, the cracked infinite hollow cylinder with an axisymmetric crack of width (b-a) is considered. The ring-shaped crack is located at the symmetry plane. Surfaces of the crack are subjected to the distributed compressive loads. The outer surface of the cylinder is rigid and the inner one is stress free. The material of the cylinder is assumed to be linearly elastic and isotropic. Integral transform techniques are used for the solution of the field equations. The resultant singular integral equation in terms of crack surface displacement derivative is converted to a system of linear algebraic equations by using Gauss-Lobatto, Gauss-Jacobi and Gauss-Laguerre integration formulas. The stress intensity factors at the tips of the crack are numerically calculated for uniform and linear load distributions on crack surfaces. Some results are presented in graphical and tabular forms.