Using single crack solution and regular plane harmonic function, the Saint-Venant bending problem of a cracked cylinder with general cross section is formulated in terms of two sets of boundary-singular integral equations, which can be solved by using the methods for combination of boundary element and singular integral equation methods. The concept of bending center used in strength of materials is extended to this bending problem. Theoretical formulae to calculate the bending center and stress intensity factors in cracked cylinder are derived and expressed by the solutions of the integral equations. Based on these results, some numerical examples are given for different configurations of the cylinder cross section as well as the crack parameters.