SUMMARY Long term deformations strongly depend on the earth model and its rheological parameters, and in particular its viscosity. We give the general theory and the numerical scheme to compute them for any spherically non-rotating isotropic earth model with linear rheology, either elastic or viscoelastic. Although the Laplace transform (LT) is classically used to compute viscoelastic deformation, we choose here instead, to implement the integration with the Fourier transform (FT) in order to take advantage of the fast FT algorithm and avoid some of the LT mathematical difficulties. We describe the methodology to calculate deformations induced by several geophysical signals regardless of whether they are periodic or not, especially by choosing an adapted time sampling for the FT. As examples, we investigate the sensitivity of the displacements due to long period solid Earth tides, glacial isostatic adjustment and present-day ice melting, to anelastic parameters of the mantle. We find that the effects of anelasticity are important for long period deformation and relatively low values of viscosities for both Maxwell and Burgers models. We show that slight modifications in the rheological models could significantly change the amplitude of deformation but also affect the spatial and temporal pattern of the signal to a lesser extent. Especially, we highlight the importance of the mantle anelasticity in the low degrees deformation due to present-day ice melting and encourage its inclusion in future models.