Predictions of geometric characteristics and elastic properties of patterns in woven fabric composites are proposed based on unit cells. This study addresses the optimization of the elastic properties within woven fabric composite unit cells with multiple designs based on periodic boundary conditions and evolutionary algorithms. Furthermore, the study permits a reliable prediction of mechanical behavior of woven fabric composites unit cells in which the weave patterns are the variables. The models are treated as a single-ply for each weave pattern embedded in a matrix pocket. The analyzed weave patterns are created by TexGen, the simulation is done with ABAQUS. At the unit cell level, effective elastic properties of the yarn were estimated from Finite Element (FE) simulations using periodic boundary conditions. An evolutionary algorithm is adopted in optimizing the elastic properties of woven fabric composites with recombination and mutation operators. We present a parameter study to investigate the effect of various geometric parameters. Those parameters include the gap length, the shape of the yarn section, the yarn thickness, the constituent materials, the fiber volume fraction and the elastic properties. By examining this optimized model through the pre-determined parameters as mentioned above, an optimal parameter set for composite's performance can be properly selected.