Dynamic analyses of four, eight and twelve storey masonry shear walls supported on base-isolation systems are described. Each wall was modelled as a multi-degree-of-freedom cantilever. Results are presented which indicate behaviour is more complex due to the significance of higher mode effects, than was previously believed on the basis of simple single-degree-of-freedom models. The influence of different types of base-isolation, and of the stiffness of the gravity supporting system, are discussed. Tentative design recommendations are proposed which provide a substantial reduction in design forces for short period structures while still maintaining an adequate margin of safety against the formation of wall hinges.