Partially restrained seismically isolated continuous (PRSI) bridges are a particular class of isolated bridges in which isolation bearings are placed only between the superstructure and the piers, while steel-plate stoppers or other devices restrain the transverse motion of the deck at the abutments. This study illustrates a simplified model for the preliminary assessment and design of these systems. The dynamic problem of PRSI bridges is described in a variational form, in order to obtain a simplified solution based on a pre-fixed transverse deformed shape of the deck. Simple formula are derived for estimating the seismic response quantities of interest. Additional formula are also proposed to account for the contribution of higher modes ...