In this paper, a lower-order singular BEM based on original BEM is presented by introduccing a new variable of angle. In the new method, kernel of force is the same as kernel of displacement which is only singularity of InR ( R is the distance between a source and a field point ) . Hence, it results in a new BEM formulation, whose singularity is lower than that of the original BEM formulation. What's more, in calculating stress, it eliminates the boundary-layer effect in the main. A software which is based on lower-order singular formulation is used to analysis the bar of 300T coiningmachine, its result is coincident with that obtained by the original BEM and photo-elastic experiment.