In the present paper, passive control technique such as base isolation system is studied under earthquake ground motions and underground blast-induced vibrations. The performance of the lead rubber bearing (LRB), idealized as Bouc–Wen model in mitigating the structural responses of a five-storey building model, is investigated. The earthquake ground motions are selected from ground motion database available on the portal COSMOS Virtual Data Centre, whereas the underground blast is modeled as an exponential decaying function as prescribed by Carvalho and Battista (Proc Inst Civ Eng Struct Build 156(3):243–253, 2003). The aim of the study is to analyze the effect of isolation parameters such as damping ratio, yield strength, post-yield stiffness ratio and yield displacement on the structural responses of the base-isolated building. Newmark’s step-by-step integration method is adopted to evaluate the structural responses of the building. It is observed that the LRB is very effective in reducing the structural accelerations and storey drifts induced in the building due to ground-induced vibration. The comparison of results show that high value of yield strength harvests low bearing displacement and low percentage reduction in the top floor absolute acceleration. In addition, the study also evaluates the energy dissipated by the isolated structure. The energy dissipated by the base-isolated (LRB) building subjected to blast-induced vibrations, show that an optimum value of yield strength is found to be in the range of 10–20% of the total weight of the structure.