The continuous variation of viscosity with depth expected from microphysical theories of silicate creep differs significantly from the layered structures typically used to model post-glacial relative sea level variations and to refine models of ice load histories. Here we predict relative sea level (RSL) curves for a set of realistically parameterized continuous viscosity profiles with different amounts of depth dependence. We demonstrate by forward modeling that different classes of realistically parameterized mantle viscosity structures are resolvable by RSL at the edge sites, but the predicted RSL there is very sensitive to the assumed ice load history. Furthermore, the sensitivity of RSL variations at these sites to the viscosity structure depends strongly upon the ice model. At sites less sensitive to the ice model, the resolving power for viscosity structure is also less. When ICE-1A, an ice model derived without assumption of mantle viscosity structure, is used to compute RSL variations, some models with realistic continuous viscosity increases with depth fit the observations better than the ''standard model'' used to derive more recent ice models. ¿ American Geophysical Union 1996