A mathematical-computational method for determining the volume, mass, and center of mass of any bilaterally symmetric organism is presented. Cavities within the body of an organism such as lungs are easily accommodated by this method. Sagittal and frontal profiles, obtained from tracings of "fleshed-out" skeletal reconstructions, are used to provide limits for defining transverse slices of the body. Any internal cavities are defined by their own sagittal and frontal profiles. The computations consist of mathematically slicing the body and any cavities into independent sets of transverse laminae and computing their masses, centroids, and moments with respect to the three coordinate axes. Further calculations produce the masses and the (x, y, z) coordinates for the centers of mass of the body, any cavities, and the body+cavities. Predicted body masses of large, extant mammals (elephant, giraffe, hippopotamus, and rhinoceros) are in close agreement with actual body masses. New, lower estimates for body masses of selected large dinosaurs, based on modern skeletal reconstructions, are also presented, along with numerical estimates of their centers of mass. This method is an improvement over earlier ones that relied on measuring displaced volumes of water or sand by scale models to estimate the masses, and suspending models by threads to estimate their centers of mass.