The dual reciprocity method (DRM) is a technique to transform the domain integrals that appear in the boundary element method into equivalent boundary integrals. In this approach the non-linear terms are approximated by an interpolation applied to the non-Newtonian stress tensor for an inelastic fluid. In the present paper we introduce a radial basis function interpolation scheme for the velocity field that satisfies the continuity equation (mass conservative interpolation). The proposed method performs better than the classical interpolation used in the DRM approach to represent such field. The new scheme together with a sub-domain variation of the DRM yields a more accurate solution for inelastic non-Newtonian problems.