An explicit weakly compressible SPH method is introduced to study movement of suspended solid bodies in Oldroyd-B fluid flows. The proposed formulation does not need further stabilizing treatments and can be efficiently employed to study particulate flows with Deborah to Reynolds number ratios up to around 10. A modified boundary treatment technique is also presented which helps to deal with the movement of solid particles in the flow. The technique is computationally efficient and gives an improved evaluation of fluid-solid interaction forces. A number of test cases are solved to show performance of the proposed method in simulating particulate viscoelastic flows containing circular and non-circular cylinders. The effect of Deborah number on the particle trajectory has been investigated. (C) 2011 Elsevier B.V. All rights reserved.