In principle, the reliability of complex structural systems can be accurately predicted by Monte Carlo simulation. This method has several attractive features for structural system reliability, the most important being that the system failure criterion is usually relatively easy to check almost irrespective of the complexity of the system. However, the computational cost involved in the simulation may be prohibitive for highly reliable structural systems. In this paper a new Monte Carlo based method recently proposed for system reliability estimation that aims at reducing the computational cost is applied. It has been shown that the method provides good estimates for the system failure probability with reduced computational cost. In a numerical example the usefulness and efficiency of the method to estimate the reliability of a system represented by a nonlinear finite element structural model is presented. To reduce the computational cost involved in the nonlinear finite element analysis the method is combined with a response surface model.