Application of limb-fitting methods to the 11 best Voyager 2 images of Enceladus has shown that the shape of this satellite is closely represented by a triaxial ellipsoid. The observed ratio of the differences of the principal axes F = (b - c)/(a - c) is 0.23+0.04-0.01, consistent with the value F = 0.23 expected for a synchronously rotating satellite in hydrostatic equilibrium. We also deduce from the Voyager observations, after allowing for limb topography, that the mean radius of the satellite is 249.4 ± 0.2 km. For satellites of known mass, measurement of the size and shape leads to a determination of the satellite's mean density and moment of inertia. We have used this method to determine the moments of inertia of Mimas (Icarus 73, 25-65, 1988) and Tethys (Icarus 94, 391-398, 1991). Enceladus appears to be hydrostatically relaxed, making it an ideal candidate for this type of analysis. However, none of the Pioneer or Voyager spacecraft had a close encounter with this satellite and thus its mass is effectively unknown. Enceladus is trapped in a 2:1 orbit-orbit resonance with Dione, but the amplitudes of libration are too small to allow a useful mass determination. Using the observed shape alone, without any other assumptions other than that the satellite is in hydrostatic equilibrium at its present orbital radius, we place an upper bound on the mean density of 1.12 ± 0.05 g/cm3. Thus, the mean density of Enceladus is probably little more than that of water-ice and we conclude that this satellite is markedly deficient in rock. If the mass of a satellite is unknown, but the satellite is differentiated and has a deep mantle of known composition, then we show that measurement of the shape alone can lead to a determination of the satellite's mass, mean density, and moment of inertia. Application of this method to Enceladus, assuming that the satellite has a deep mantle of water-ice of density 0.93 g/cm3, gives the result that the mean density of the satellite is 1.00 ± 0.03 g/cm3. This result fills the one remaining gap in our knowledge of the structure of the Saturnian satellite system. We now know the mean densities of all the primary Saturnian satellites in the sequence from the coorbital satellites, Janus and Epimetheus, through to the outer satellite Iapetus (the densities of the small, secondary satellites in Trojan-type orbits are still unknown). The Saturnian system possesses two striking features. (1) Because of significant porosity, the mean material densities of the satellites Janus, Epimetheus, and Mimas could be substantially greater than the apparent mean densities of these satellites. (2) The densities of the satellites are not correlated with their distances from the planet; in particular, the satellites Enceladus and Tethys have lower mean densities than their interior and exterior neighbors, Mimas and Dione. This may be the result of gross postformation redistribution of rock and ice, possibly due to satellite disruptions as suggested by Smith et al. (Science 215, 504-537, 1982).