Abstract. The development of methods that allow to numerically reproduce the actual behavior of real structural systems has challenged scientists and researchers and urged them to address issues that extend beyond the integrity of a system. Therefore, a series of new parameters must be taken into account to evaluate the failure of a real structural system, especially in redundant systems. In the present paper, an accurate technique is developed to satisfy the probabilistic analysis. The proposed method estimates the reliability of the system with techniques that enable detecting multiple failure modes and, using the chi-squared distribution, a one direction exact integration is performed to calculate the failure probability of each mode in a more precise way than conventional approximation and simulation methods. This technique is based on the conventional (HDM) Hyperspace Division Method procedures which approximate the limit state surface by a series of spherical segments for provide accurate estimates of failure probabilities of components or systems. Besides, in this work, nonlinearity is considered by adopting an elastic plasticity model with linear hardening. Numerical applications showed the accuracy and efficiency of the methodology in the evaluation of the failure probability of problems represented by high nonlinear limit state functions with multiple failure regions.