In this study, numerical simulations are performed to study the effects of body shape on propulsive performance in a carangiform-like swimming motion. A focus is given to the variation in performance due to changes in the maximum thickness, maximum thickness location, leading-edge radius, and boattail angle of an undulating foil. An immersed boundary method-based incompressible flow solver is implemented to solve for the propulsive performance of two-dimensional undulating foils. The resulting flow simulations yield the thrust, drag, efficiency, and flow for each body shape. From this study, we have found that better propulsive performance comes from a thinner maximum thickness, a maximum thickness location closer to the head of the fish, a narrower boattail angle, and a larger leading-edge radius. Particular care is given to the analysis of the boattail angle, because of the surprising and significant results. In changing only the boattail angle the efficiency is shown to vary by 10.3%. Changes in the leading-edge radius varies the efficiency by 4.4%, the maximum thickness by 4.0%, and the maximum thickness location along the body by 5.0%. The large improvement observed in the thinner boattail angle cases are caused by the increased curvature around the middle of the fish body leading to a high-pressure region at the tail that improves the thrust performance. The results can be used to improve understanding of fish body shapes observed in nature as well as better informing the design of bio-inspired underwater robots.