Summary This paper focuses on the performance of shape-memory-alloy rubber bearings (SMARBs) compared to conventional lead-plug or New-Zealand (N-Z) bearings in control of building vibration due to underground blast induced ground motion (BIGM). The performance is evaluated with regard to maximum acceleration and isolator displacement obtained by nonlinear time history analysis. In doing so the Bouc–Wen's model is used to represent the nonlinear behaviour of the N-Z bearing and the superelastic behaviour of nickel–titanium-based shape-memory alloy is represented by the Graesser–Cozzarelli model. The underground BIGM input is modelled by exponentially decaying function. It is observed that though the N-Z bearing is fairly effective in controlling the structural accelerations due to BIGM without excessive bearing displacements, there remains a problem with the residual bearing displacements. The latter, however, is found to be dealt with very effectively by the SMARB. Furthermore, the procedure to obtain the optimum design parameters of the base isolators under study is obtained by optimizing two mutually conflicting objective functions, that is, the minimization of peak acceleration as well as peak bearing displacement by converting the multiobjective optimization problem to a single composite objective function. The improved and robust control performance of SMARB compared to N-Z bearing is elucidated through numerical study by considering a five-storied shear building frame.