This thesis is concerned with characterizing the compression stiffness and compression strength of 2D tri-axially braided textile composites (2DTBC). Two types of 2DTBC are considered differing only on the resin type, while the textile fiber architecture is kept the same with bias tows at 45 degrees to the axial tows. Experimental, analytical and computational methods are described based on the results generated in this study. Since these composites are manufactured using resin transfer molding, the intended and as manufactured composite samples differ in their microstructure due to consolidation and thermal history effects in the manufacturing cycle. These imperfections are measured and the effect of these imperfections on the compression stiffness and strength are characterized. Since the matrix is a polymer material, the nonuniform thermal history undergone by the polymer at manufacturing (within the composite and in the presence of fibers) renders its properties to be non-homogenous. The effects of these non-homogeneities are captured through the definition of an equivalent in-situ matrix material. A method to characterize the mechanical properties of the in-situ matrix is also described. Fiber tow buckling, fiber tow kinking and matrix microcracking are all observed in the experiments. These failure mechanisms are captured through a computational model that uses the finite element (FE) technique to discretize the structure. The FE equations are solved using the commercial software ABAQUS version 6.5. The fiber tows are modeled as transversely isotropic elastic-plastic solids and the matrix is modeled as an isotropic elastic-plastic solid with and without microcracking damage. Because the 2DTBC is periodic, the question of how many repeat units are necessary to model the compression stiffness and strength are examined. Based on the computational results, the correct representative unit cell for this class of materials is identified. The computational models and results presented in the thesis provide a means to assess the compressive strength of 2DTBC and its dependence on various microstructural parameters. The essential features (for example, fiber kinking) of 2DTBC under compressive loading are captured accurately and the results are validated by the compression experiments. Due to the requirement of large computational resources for the unit cell studies, simplified models that use less computer resources but sacrifice some accuracy are presented for use in engineering design. A combination of the simplified models is shown to provide a good prediction of the salient features (peak strength and plateau strength) of these materials under compression loading. The incorporation of matrix strain rate effects, a study of the effect of the bias tow angle and the inclusion of viscoelastic/viscoplastic behavior for the study of fatigue are suggested as extensions to this work.