Computing the reliability of structural components with uncertainties in both stress and resistance variables is investigated. The NESSUS™ probabilistic software is used to perform the reliability computations using both Fast Probability Integration (FPI) and Monte Carlo methods. Results are compared for an example reliability analysis using both closed-form expressions and finite elements. The Advanced Mean Value probabilistic algorithm is used and is shown to yield highly accurate results, even for highly nonlinear response functions. The results show clearly the effectiveness of the newly incorporated algorithms available in the NESSUS software for computing structural reliability.