The effect of non-linear rheology on surface displacements, gravitational potential perturbation and ∂tJ2 (or J2-dot) for a self-gravitating spherical earth is studied using a finite element code coupled to Poisson's equation. Four earth models investigated are: a model with uniform linear rheology throughout the mantle and three others containing nonlinear rheology in the whole mantle, upper mantle and lower mantle respectively. The effect of self-gravitation is shown to be non-negligible. The effects of nonlinear rheology in different parts of the mantle on surface displacements and potential have also been shown to be large. ∂tJ2 due to cyclic glaciation of the Laurentian, Fennoscandian, Barents Sea and Antarctic ice sheets over realistic oceans is also computed for all four rheology models. The model with nonlinear lower mantle cannot be ruled out by the observed data.