The primary goal of this research is to forecast the mechanical strength of 2 × 2 twill weave natural fiber reinforced hybrid textile composites, a critical property needed for both practical applications and production. For this purpose, a three-dimensional finite element (FE) package ABAQUS in conjunction with TexGen is employed to predict the mechanical performance of a hybrid natural fiber reinforced composites with epoxy as matrix material under compression. For various natural materials such as flax, basalt, and jute, as well as combinations of these materials (inter-yarn hybrid basalt-flax, jute-flax, and basalt-jute fabrics), a thorough FE model of a 2 × 2 twill woven fabric unit cell is constructed and examined. Out of all the hybrid combinations, basalt-flax twill weave with epoxy as the matrix material performs better mechanically under compression loading since the displacement occurred to the minimum value, which led to higher generated strain and contact pressure. The proposed FE model takes into consideration the interaction between yarns and faithfully reproduces the behavior of the fabric under compression. With respect to different weaving patterns, material characteristics, and stress conditions, the existing model can replicate a textile fabric quite well.