This study is concerned with the fracture of an axisymmetric thick-walled cylinder. The cylinder is under the action of axisymmetric tensile loads at infinity. A ring-shaped crack with surface free tractions is located at the symmetry plane. Material of the cylinder is assumed to be linearly elastic and isotropic. Solution for this problem can be obtained by superposing the solutions for (i) an infinite cylinder subjected touniformly distributed tensile load at infinity, and (ii) an infinite cylinder having a crack (the perturbation problem). The Hankel and Fourier transform techniques are used for the solution of the field equations. Applying the boundary conditions, the singular integral equation in terms of crack surface displacement derivative is derived. By using an appropriate quadrature formula the integral equation is reduced to a linear algebraic equation system. Numerical solution is used to develop results for the stress intensity factors at the tips of the crack. Results are presented in graphical and tabular forms.