We investigate the sedimentation of a sphere in a viscoelastic fluid with a cross-shear flow by numerical simulation. The non-Newtonian properties of the suspending fluid determine the settling rate of the sphere. Experiments [Tonmukayakul et al., US Patent Number US8,024,962(B2) (2010); van den Brule and Gheissary, J. Non-Newton. Fluid Mech. 49 (1993) 123-132] have shown the settling rate increases with increase in cross-shear Weissenberg number, Wi, in elastic guar gum solutions and decreases in Boger fluids. In the present work, simulations of a sheared viscoelastic flow past a sphere are used to study the effect of the shear-thinning and elasticity of the carrying fluid on the sphere's settling rate. The elastic guar gum solutions are modeled using the Giesekus constitutive model. The parameters are obtained by fitting the rheological data. The drag on the sphere decreases, i.e. the settling rate increases, with an increase in the shear Weissenberg number that is in qualitative agreement with the experiments. The decrease in the drag is primarily due to the decrease in the polymer drag component because of shear-thinning. This is in contrast with the increase in the drag in Boger fluids due to the increase in viscous drag. The effect of different polymer characteristics such as shear thinning and elasticity on the flow field is presented. There is an optimum value for the amount of polymers in the solution for the increase in the viscous drag to overcome the decrease in the polymer drag leading to a net increase in the drag on the sphere. The effect of walls on the drag coefficients in Boger fluids is also investigated. It is demonstrated that the effect of the increase in the drag coefficients with Wi is accentuated as the interaction with the wall grows stronger. The wall interactions lead to an increase in viscous shear stresses downstream of the sphere, which causes the increase in the drag. (C) 2013 Elsevier B.V. All rights reserved.