The compressive response of 3D woven textile composites (3DWTC), that consist of glass fiber tows and an epoxy matrix material, is studied using a finite element (FE)-based mechanics model. A parametric Representative Unit Cell (RUC) model is developed in a fully three-dimensional setting with geometry and textile architecture for modeling the textile microstructure. The RUC model accounts for the nonlinear behavior of the fiber tows and matrix. The computational model is utilized to predict the compressive strength of 3DWTC and its dependence on various geometrical and material parameters. The finite element model is coupled with a probabilistic analysis tool to provide probabilistic estimates for 3DWTC compressive strength. The reported results are found to be in good agreement with experimental data.