The settling rate of heavy spheres in a shear flow of viscoelastic fluid is studied by numerical simulation. Experimental data [Tonmukayakul et al., US Patent Application US20110219856 (2011); van den Brule and Gheissary, J. Non-Newton. Fluid Mech. 49 (1993) 123-132] have shown that both shear thinning and the elasticity of the suspending polymeric solutions affect the settling rate of the solids. In the present work, simulations of viscoelastic flow past a single, torque-free sphere with a cross shear flow are used to study the effect of the elasticity of the carrying fluid on the sphere's settling rate. The FENE-P constitutive model is used to represent a viscoelastic Boger fluid, with parameters obtained by fitting rheological data. A twofold increase in drag, i.e. a decrease in settling rate, is obtained with increase in the cross shear Weissenberg number, Wi <= 15, even though the shear viscosity of the solution decreases over this same range. At small Weissenberg number, Wi < 2, the simulations remain in quantitative agreement with the experiments. At higher Weissenberg number, the numerical results remain in qualitative agreement with settling experiments although the magnitude of the simulated decrease in settling rate is smaller than that observed in experiments. The detailed physical mechanism for the increase in the drag experienced by the sphere in the simulations is presented and we show that tau(11) component of the viscous stress (with 1, the sedimentation direction) is the primary cause of the increase in sphere drag. (C) 2013 Elsevier B.V. All rights reserved.