In recent times, Carbon fiber reinforced polymers (CFRP) are widely adopted in various industries such as automobile, aerospace, marine, infrastructure, etc. due to their excellent strength to weight ratio. On the other hand, woven textile composites are replacing unidirectional composites since the fiber can be reinforced in more than one direction. To improve the mechanical behavior of CFRP woven composite materials, it is crucial to investigate their constituent properties at micro-level considering fiber material, fiber volume fraction, yarn volume fraction, yarn spacing, fabric thickness, etc. along with the type of weaving, such as plain, twill or satin. In this present research, a computational homogenization technique based on commercial finite element code Ansys is adopted to investigate the effect of constituent properties on the elastic modulus of plain and twill woven composites considering two different carbon fibers; namely, Carbon-290 and Carbon-395. Numerical results reveal that both fiber volume fraction and yarn volume fraction have a strong effect on the prediction of in-plane elastic modulus of CFRP composites. However, fabric thickness does not impact the prediction at all, while yarn spacing has a minor effect on the outcomes. Moreover, the weaving type does not affect the predictions significantly. Finally, it is found that Carbon-290 fiber provides higher elastic modulus values for any given condition than Carbon-395 fiber.