Linear stress analysis without body force can be easily solved by means of the boundary element method. Some cases of linear stress analysis with body force can also be solved without a domain integral. However, domain integrals are generally necessary to solve the linear stress problem with arbitrary body forces. This paper shows that the linear stress problem with arbitrary body forces can be solved approximately without a domain integral by the triple-reciprocity boundary element method. In this method, the distribution of arbitrary body forces can be interpolated by the integral equation. A new computer program is developed and applied to several problems.