In this paper, the complete double layer boundary integral equation formulation for Stokes flows is extended to viscoelastic fluids to solve the mobility problem for a system of particles, where the non-linearity is handled by particular solutions of the Stokes inhomogeneous equation. Some techniques of the meshless method are employed and a point-wise solver is used to solve the viscoelastic constitutive equation. Hence volume meshing is avoided. The method is tested against the numerical solution for a sphere settling in the Odroyd-B fluid and some results on a prolate motion in shear flow of the Oldroyd-B fluid are reported and compared with some theoretical and experimental results. / Singapore-MIT Alliance (SMA)