The paper presents a method for evaluating the dispersion and reliability of structural analysis using a statistical optimization method that consists of effectivity analysis and optimization. The effectivity analysis is used to generate approximate evaluation functions for the behavior of an object structure. A first-order second-moment method is employed to evaluate and generate approximate evaluation functions for the dispersion of the behavior. A successive quadratic programming (SQP) method is employed to solve the optimization problem using the approximate evaluation functions of the behavior with dispersion. A reliability index β, β^* and the upper bound of failure probability obtained using the second moment method are employed in the reliability evaluation of the object structure with a set of design parameters. It is confirmed that the proposed method can be used for almost all kinds of nonlinear problems including the impact behavior of structures, and that the number of finite element analyses based upon the proposed method is much smaller than that of other existing methods.