The stochastic response of a one-storey model of a base isolated asymmetric building to random ground excitation is computed using the state space formulation. Three types of base isolation devices are considered: the laminated rubber bearing (LRB); the New Zealand system (NZ); and the resilient-friction base isolator (R-FBI). For the NZ and R-FBI systems, for which force-deformation behaviour is nonlinear, an equivalent linearization technique is applied to obtain an approximate response. The effect of linearization on the response is investigated by comparing the responses of the linearized solution with those obtained from simulation analysis. The RMS responses of the system are obtained under different parametric variations in order to investigate the effectiveness of different base isolation devices for stationary random ground motion. The study shows that the stochastic response of the asymmetric building isolated by an R-FBI system is less sensitive to the parametric variations.