We present a novel Lagrangian finite element method for simulating suspensions of particles in viscoelastic fluids. We solve the flow in a unit cell containing a small number of particles with doubly periodic boundary conditions on a self-replicating two-dimensional lattice to replicate a suspension on an infinite domain. The method uses a Lagrangian finite element grid that deforms with fluid combined with a quotient representation of the periodic lattice. We show that qualitatively different results are obtained for the shear-thinning pompom constitutive equation compared to those obtained using the Oldroyd B fluid. For the pom-pom fluid we show that the changes to shear viscosity with the addition of particles can be obtained by a simple shifting of the shear-rate and shear-stress.