Epoxy carbon fiber composite materials are known for their light weight and high performance. They can be effective substitutes for commonly used materials for making drive shafts. Fiber orientation angle plays a major role in determining such a drive shaft’s responses. The responses considered in this paper are critical buckling torque, fundamental natural frequency and total deformation. A drive shaft made of epoxy carbon unidirectional prepreg is generated using ANSYS 18.0 ACP Composite Prepost. The objective of this paper is to determine an optimal configuration of fiber orientation angles for four, five and six-layered epoxy carbon drive shaft which tends to increase critical buckling torque and fundamental natural frequency while decreasing the total deformation. The optimal configuration which satisfies this objective for the three responses is identified by Minitab 17 statistical software. The effect of fiber orientation angle with respect to each of these responses is studied in detail. Finally, a hybrid shaft is considered with aluminium 6061-T6 alloy tube on the exterior and 4 layers of epoxy carbon layers stacked up in optimal configuration in the inside. The hybrid shaft is found to satisfy all the design constraints with appreciable weight reduction compared to conventional KS SM45C steel drive shaft.