Recently, an increasing interest in materials filled with solid particles is observed. Addition of rigid particles to a liquid alters the flow field and hydrodynamic effects lead to strong variations in the rheological properties. In several applications, the suspending fluid shows a non-Newtonian behaviour, further complicating the overall rheological response of such materials. Aim of the present thesis is to analyze the rheology and the dynamic of a suspension of solid particles dispersed in a viscoelastic medium through numerical simulations. In the first part, the rotation of a single sphere in a sheared viscoelastic medium and the resulting rheology are studied. The results show a slowing down effect of the particle rotation rate related to the fluid viscoelasticity. In the second part, solid concentrated suspensions in planar elongational flows are investigated. A new efficient method to take into account the boundary conditions is devised. For a viscoelastic suspending fluid, the bulk elongational viscosity is found to be an increasing function of solid area fraction and fluid viscoelasticity. Nevertheless, a less and less pronounced strain hardening is found as the solid concentration increases. The simulations successfully predict the experimental observations reported in literature.