Carbon fiber-reinforced composite stringers, which support aircraft skins in resisting tensile, compressive, and shear loads, are widely used in aircraft structures. These composite structures play a crucial role in enhancing the performance and safety of the structural integration of aircrafts. To better understand the load-bearing capacity of composite stringer structures, this study developed a novel model to study the complex failure and load transmission behavior of T800/3900S-2B fiber-reinforced composite skin-stringer structures under compressive loading. Compression strength tests were conducted on a composite stringer/skin structure, and a three-dimensional FEM was developed using Abaqus/Standard 2022. The model incorporated the modified 3D Hashin initiation criteria and Tserpes degradation law through a UMAT subroutine, which can effectively capture the in-plane ply failure and interlaminar damage. The results revealed a high degree of similarity between the load–displacement curves and failure modes (i.e., matrix compressive cracking, fiber compressive failure, and fiber–matrix shear-out failure) obtained from the simulations and those from the experiments. This study provides an efficient and accurate model to simulate the failure and load transfer of composite skin-stringer structures, offering significant advancements in understanding and predicting the behavior of these critical components.