The mechanism for shear thickening of the viscometric functions of rigid non-Brownian sphere suspensions in highly elastic fluids is studied numerically. Particular focus is placed on the particle-induced fluid stress, which is the dominant contribution to the shear thickening behavior, especially at moderate to high Weissenberg numbers. We determine the Weissenberg number scaling for both the magnitude of the particle-induced fluid stress and the volume containing most of the particle-induced fluid stress to understand the overall suspension behavior at moderate Weissenberg numbers. Furthermore, we analyze the flow type in the regions of significant polymer-induced fluid stress and find that the stretch of polymers in strain-dominated flow within closed streamlines around the particles generates the large stresses that contribute to the thickening behavior. Thus, understanding the response of the suspending fluid to extensional deformation is important for predicting the shear rheology of the bulk suspension. Lastly, we explore the effect of polymer viscosity and polymer extensibility on the behavior of the particle-induced fluid stress. (C) 2018 The Society of Rheology.