The studies have been carried out on the damage initiation behavior of polymer matrix woven fabric composite plates subjected to a transverse central low velocity point impact load. Specifically, the effect of incident impact velocity and impactor mass for the same incident impact energy on the impact behavior has been investigated with a square plate of 150 mm × 150 mm × 6 mm. The material systems considered are: E-glass/epoxy and T300/5208 carbon/epoxy woven fabric composites. Inplane failure of the layers in the form of matrix cracking / lamina splitting and delaminations were the primary objectives of the study. The studies have been carried out using an in house Finite Element Analysis code. The inplane failure functions and the interlaminar failure functions have been predicted using quadratic failure criteria. It is observed that the use of incident impact energy alone as a parameter to characterize the impact behavior is inadequate. Instead, the effect of both incident impact velocity and impactor mass should be considered separately.