The predictive capability of a progressive damage model to simulate the quasi-static and dynamic crushing of composite specimens is evaluated in this article. The material model is commercially available within the ABAQUS finite element software package, i.e., “Damage for Fiber reinforced Composites”, and is often utilized to simulate damage progression and failure in static and dynamic failure scenarios such as crushing of a composite plate. The composite specimens used in this study consist of quasi-isotropic C-shaped and corrugated composite panels comprised of carbon fiber/epoxy braided fabric. The C-shaped panel specimen is used to calibrate the model and optimize material/model properties through comparison with experimental results. Then, using the same model parameters, the quasi-static crush response of the corrugated panel is predicted. The predictive capability of the model is further demonstrated by simulating the dynamic crushing response of both C-shaped and corrugated panels using the same material properties as in the quasi-static crush case with only minor adjustments for the dynamic elastic properties (i.e., rate dependent modulus). Results show that the in-built material model available in ABAQUS can successfully reproduce experimental results for both panels (C-shaped and corrugated) subjected to both quasi-static and dynamic loading scenarios. A small-scale parametric study on physical (experimentally measurable) and nonphysical (purely mathematical) model parameters was also conducted. It can be concluded that, achieving successful simulation results requires a more in-depth understanding of the influence of model parameter variation on the mechanical response of the composite together with the strategies and challenges of the utilized modeling methodology (e.g., FEA mesh density, etc.).