The number of stacked plies and orientations of carbon fiber/epoxy in a sandwich panel with an aluminum honeycomb core was optimized using finite element analysis to improve the structural performance of the monocoque chassis for the electric Formula SAE racecar. To establish the selection criteria for fabrics and orientations, the single unidirectional (UD) and woven plies (W) were simulated under tensile and simple shear tests to determine their off- and on-axis properties. Simulation results revealed that the unidirectional ply enhances the overall strength of laminate, while woven ply is responsible for shear strength. Thus, the combination of unidirectional and woven plies was proposed. The four anisotropic laminates consisting of four stacked plies with different orientations were simulated under three-point bending and plate twist tests to determine the flexural rigidity and twist stiffness, respectively. Their mechanical properties were then compared to the quasi-isotropic laminates of four symmetrical unidirectional plies and four symmetrical woven plies, as well as the orthotropic laminates consisting of four unidirectional plies, and four woven plies. The four-ply UD stack exhibited the highest flexural strength of 123 MPa but a smaller twist stiffness, 580 Nm, than that of other anisotropic laminates. Moreover, the two quasi-isotropic laminates showed higher twist stiffness, 700 Nm for UD, and 820 Nm for W, than the four-ply W stack with similar fiber orientation, which showed 380 Nm. Therefore, woven plies aligned along the 45° off-axis contributed to the overall torsional stiffness of the laminate. The weights and strengths of the four anisotropic laminates were compared to the laminate containing five different orientations of plies. The specific torsional stiffness and the flexural rigidity at the side impact zone of the composite monocoque chassis were investigated. The orientations that showed high strength for the side impact zone and torsional stiffness while minimizing weight were proposed.