While many composite monocoque and semi-monocoque chassis have been built there is very little open literature on how to design one. This paper considers a variety of issues related to composite monocoque design of an automotive chassis with particular emphasis on designing a Formula SAE or other race car monocoque chassis. The main deformation modes and loads considered are longitudinal torsion, local bending around mounting points, and vertical bending. The paper first considers the design of elements of an isotropic material monocoque that has satisfactory torsional, hardpoint, and vertical bending stiffness. The isotropic analysis is used to gain insight and acquire knowledge about the behavior of shells and monocoque structures when subjected to a vehicle's applied loads. The isotropic modeling is then used to set initial design targets for a full anisotropic composite analysis. The flexibility in composite layout and core design coupled with the superior material properties of carbon fiber composites is used to design and move toward an optimized monocoque composite design and layup to obtain satisfactory torsional, hardpoint and bending stiffnesses with minimal weight. Finally, some fatigue analysis considerations are outlined with emphasis on the endurance limit of the monocoque for a specific life span. The methods presented in this paper should be helpful in designing a monocoque structure chassis for FSAE race car or other applications.