In this study, closed form equations as functions of the isolator, bridge and ground motion properties are formulated to calculate the optimum characteristic strength, Q(d) and post-elastic stiffness, k(d), of the isolator to minimize the maximum isolator displacement (MID) and force (MIF) for seismic isolated bridges (SIBS). For this purpose, first, sensitivity analyses are conducted to identify the bridge, isolator and ground motion parameters that affect the optimum values of Q(d) and k(d). Next, for the identified parameters, nonlinear time history analyses of typical SIBs are conducted to determine the optimum values of Q(d) and k(d) for a wide range of values of the parameters. Next, nonlinear regression analyses of the available data are conducted to obtain closed form equations for the optimum values of Q(d) and k(d), to minimize the MID and MIF. The equations are then simplified for various site soil conditions. It is observed that the optimum Q(d) and k(d) are highly dependent on the site soil condition. Furthermore, the optimum Q(d) is found to be a linear function of the peak ground acceleration. (C) 2011 Elsevier Ltd. All rights reserved.