The efficient evaluation of reliability index is of considerable importance in the assessment of component reliability and reliability-based structural optimization. In this thesis, the structural reliabiltiy analysis is performed using the random sampling techniques such as traditional Monte Carlo simulation and the analytical techniques such as first-order reliability method. The feasibility of Gauss quadrature points as means of target sampling of design space and generating accurate first- and second-order response surface models of failure functions is examined. Parametric uncertainty is considered by probabilistic modeling of design parameters. Various alternative approaches for estimation of component reliability index are examined with application to two structural problems: ply failure in a multidirectional composite laminate and axial buckling of a composite circular cylinder. The probabilistic sensitivity analysis is performed to measure the influence of each random variable on the estimated reliability index. The advantages and disadvantages of each approach are discussed and the approach considered the most efficient in terms of accuracy and computational requirements is identified. Furthermore, the most efficient approach is applied in reliability-based structural optimization of a composite circular cylinder with ply failure and axial buckling constraints. The optimization problem is solved using sequential quadratic programming based on sequential local response surface approximations of failure functions. The optimization results are presented for different geometric properties, laminate configurations, and coefficients of variation.