In the context of structural reliability analysis at the level 3, it is necessary to formulate full scale probabilistic models of the various random variables related to load and resistance. Often, it is convenient to work with the probabilistic models of the resultant load or resistance variable. Such models of resultant variables are presently developed by means of Monte Carlo simulation techniques. It is possible to develop analytical formulations for these probabilistic models, using classical probability theory. However, this involves the solution of multidimensional improper integrals, which are generally impractical to handle, using even the best of numerical techniques. This paper shows how the analytical formulation may be reduced to a form that is ideally suited for the convenient application of Hermite Integration, provided the basic variables follow normal or lognormal distributions. This situation is frequently encountered in practice in the case of basic resistance variables. Hence, the proposed Hermite Integration solution is well suited for the generation of the probability density function (pdf) of resistance, particularly in complex problems, where a large number of basic variables are involved. It has been shown that the vital key to the efficiency of the Hermite Integration technique lies in a judicious allocation of the various integration orders. This paper demonstrates the application of the proposed method to two practical examples. The results clearly indicate the superiority of the proposed method over the conventional Monte Carlo Simulation method in terms of computational efficiency. Furthermore, the Hermite Integration Method and the Monte Carlo Simulation method together provide useful and necessary validation of the solution developed.