Race teams are interested in understanding the influence of the various structural members on the torsional stiffness of a NASCAR Winston Cup race car chassis. In this work we identify the sensitivity of individual structural members on the torsional stiffness of a baseline chassis. A high sensitivity value indicates a strong influence on the torsional stiffness of the overall chassis. Results from the sensitivity analysis are used as a guide to modify the baseline chassis with the goal of increased torsional stiffness with minimum increase in weight and low center-of-gravity placement. The torsional stiffness of the chassis with various combinations of added members in the front clip area, engine bay, roof area, front window and the area behind the roll cage was predicted using finite element analysis. Torsional stiffness increases and weight from several competing chassis designs are reported. Twist angle and the rate of change in twist angle under torsion is calculated at several locations along the frame. With strategic placement of structural members to a baseline chassis, the torsional stiffness can be more than tripled with only a 40 lb increase in weight.