This study develops a sophisticated three-dimensional elastoplastic progressive damage finite element analysis (FEA) model for stiffened composite materials under axial compression. The model integrates the Hashin and Ye criteria to capture the inception of damage within the composite and introduces a cohesive zone model (CZM) to simulate debonding between stiffeners and panels. Furthermore, damage evolution based on energy release rate and plastic flow rules grounded in Hill's criteria are employed to thoroughly explore the progressive failure behavior of stiffened composite materials. Implemented within Abaqus/Explicit through user-defined 'VUMAT' subroutines, the model ensures computational accuracy and reliability. Comparative evaluations against standard linear elastic progressive damage models demonstrate a statistically significant improvement of at least 5% in predicting ultimate load capacities. Additionally, this model accurately captures different failure modes, providing a nuanced understanding of stiffened composite material failure under compressive loads.