By using the weak form of the governing equations for sectorial bimaterial domains and assuming that the displacement field is proportional to the (λ+1)th power of the distance from the singular stress point, a second-order characteristic matrix equation on λ is derived by a one-dimensional finite element formulation that only discretizes the domain circumferentially. Numerical examples covering a variety of interfacial singularities are presented to demonstrate the efficacy of the formulation. Accurate solutions are yielded by very few elements whereas convergence can be attained by either h- or p-refinement. The related procedures are programmed in a short MAPLE worksheet given in the appendix.postprin