A robust and sophisticated structural reliability evaluation procedure is presented. Reliability of any structural systems represented by finite elements can be evaluated using the algorithm. The authors called it a stochastic finite element method. Despite the significant recent progress in the risk and reliability analysis techniques, a large segment of the engineering profession is not familiar with them and thus fails to use them in everyday practices. The procedure is expected to fill that vacuum. Many sources of nonlinearity generally overlooked in the profession can be incorporated in the algorithm. Uncertainties in the load and resistance-related variables are modeled as realistically as possible. The estimation of the failure probability implies that structural behavior just before failure needs to be captured as accurately as possible. The algorithm is capable of evaluating the probability of failure addressing all the related issues. With the help of four informative examples, the application potential of the procedure is clearly demonstrated. It is similar to the deterministic methods and is not expected to be complicated to the practicing engineers; thus, promoting its wider applications. It is shown that the observations made in laboratory experiments can be explained with the procedure. It is hoped that the method will be used in the future to estimate the reliability of real structures.