The mantle of the earth is rheologically similar to an amorphous polymer. The short‐time‐scale behavior in shear is anelastic and rather well described by a constant Q absorption band. The long‐time‐scale behavior is essentially Newtonian viscous and this mode of deformation dominates the material behavior for times in excess of a Maxwell time which is on the order of 200 years. Most geophysical observations seem to be adequately reconciled by a simple linear viscoelastic rheology which is a generalization of the classical Burger's body and which is uniformly valid in time. This model is particularly useful because there exists a simple analytic expression for the shear modulus in the Laplace transform domain so that correspondence principle methods may be easily applied to solve dynamical problems. This article provides a simple derivation of this expression for the shear modulus and demonstrates the manner in which the unknown rheological parameters may be determined by fitting appropriate geophysical observations. Particular attention is devoted to discussion of the long‐time‐scale viscous response which is a crucial ingredient in the thermal convection hypothesis of continental drift.