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The true shapes of elliptical galaxies cannot be determined from photometric data alone. Here I present a new general method for constraining the intrinsic shapes of ellipticals through their apparent shapes and kinematics. At its heart is a set of theoretical models for radial velocity fields, constructed by solving the equation of continuity for the mean flow of the stellar ``fluid''. The radial luminosity profile, halo density profile, axis ratios, rotation axis, and other dynamical parameters may be chosen freely; radial mean motions induced by aspherical dark halos can be included. The primary simplifying assumption is that the three-dimensional flow field is similar at all radii well outside the core. The models are both more general and much easier to calculate than the existing, very restrictive, self-consistent models. The quick computability makes it possible to develop a procedure of Monte Carlo model fitting that compares models and real galaxy data in a statistically rigorous way. Typically $10^7$ individual models are compared against the data in a complete shape fit. It is found that, with standard photometry and high-quality kinematics at 4 position angles, the shapes of individual ellipticals can be estimated despite ignorance of their detailed internal dynamics and halo structure. This claim is illustrated with the E2 galaxy NGC 4589. The dynamical triaxiality $T$ and the flattening of the light distribution $c_L$ are found to be $T = 0.63 \ ^{+.28}_{-.43}$, $c_L = 0.80 \ ^{+.05}_{-.12}$ ($1\sigma$ errors), making the most probable shape prolate-triaxial. The dominant source of error is in the measured velocities. Reducing the errors to 15\% of the maximum rotation velocity would shrink the uncertainty in shape by a factor of 2. Results for the Virgo elliptical NGC 4472 (M49) are also presented.
