Abstract Six-noded isoparametric finite elements are used to estimate singularity powers for problems with known solutions. The effect of crack length to crack tip element ratios as well as mesh refinement are shown to produce slight deviations in estimates of the singularity power. The bi-material problem with a crack terminating at the interface is investigated. Estimates of the singularity power for various material combinations are presented. A method of possibly improving singularity power estimations using finite elements is discussed.