This thesis presents a Stochastic Finite Element Method (SFEM) framework to improve the reliability analysis of composite materials, accounting for material uncertainties which often arise from manufacturing imperfections. These uncertainties lead to discrepancies between experimental and numerical results, typically addressed through conservative safety factors. The framework integrates the Karhunen-Loève (KL) expansion to model spatial variability in material properties and Latin Hypercube Sampling (LHS) for efficient probabilistic simulations. Two KL expansion methods are compared - the Galerkin and Bounding Box approaches - and the latter is found to be more computationally efficient. A continuum damage model (CDM) simulates progressive failure in composite laminates, and the methodology is validated through test cases such as Open Hole Tension. The results show that incorporating spatial material variability leads to more accurate predictions of failure probabilities, potentially enabling reduced conservatism in the design phase. This work supports the use of stochastic methods for improving reliability-based design of composite structures.