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). This formulation required more than 13000 nonlinear time history analyses of simplified SIB models. The analyses results revealed that the optimum Qd and kd are highly dependent on the site soil conditions and peak ground acceleration of the ground motion.