The use of structural reliability methods with implicit limit state functions (LSFs) shows the increasing demand for efficient stochastic analysis tools, because the structural behaviour predictions are often obtained by finite element analysis. All stochastic mechanics problems can be solved by Monte Carlo simulation method, nevertheless, in most cases, at a prohibitively high computational cost. Several approximations can be achieved using first-order reliability method (FORM) and second-order reliability method and response surface methods. In this paper, a method that combines the FORM and Kriging interpolation models, as response surface, is proposed. The prediction accuracy of the Kriging response surface obtained from different sampling techniques is assessed, and the failure probability estimates calculated by the FORM using the classical second-order polynomial regression models and the Kriging interpolation models as surrogates of nonlinear LSFs are compared. The usefulness and efficiency of the reliability analysis using the Kriging response surface are demonstrated on the basis of existing results available in the literature and with an application problem of a stiffened plate structure with initial imperfections.