The flow of a viscoelastic fluid, which is simulated by a Criminale-Ericksen-Filbey model, between two concentric rotating spheres is analyzed theoretically. This problem has wide applications in practice. The assessment of the performance of a polymerization reactor, for example, requires knowledge about the rheological properties of the reacting fluids and flow patterns around agitators. We show that the shear-thinning effects of both the viscosity and the elasticity of a fluid may lead to double-vortex flows. The origin of these vortices are discussed, and the effect of the relative sizes of the inner and the outer spheres on the vortex flows is investigated. The influence of the elasticity on the torque required to rotate the spheres is also evaluated.