Abstract: Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques are employed to formulate a circular singular analytical element. The analytical element gives a precise description of the displacement and stress fields in the vicinity of plane crack tip for the plane crack problem. The new analytical element can be implemented into FEM program systems to solve for stress intensity factor and deal with crack propagation problems for plane cracks with arbitrary shapes and loads. Numerical results for typical problems show that the method is simple, efficient and accurate.