Exact elastodynamic theories for fluid loaded elastic shells are only amenable to solution for simple geometries. If separation of variables methods or the extended boundary condition techniques can not be used then alternative numerical techniques are very time consuming and filled with numerical pitfalls. On the other hand the more tractable approximate shell theories (used in place of the exact theory) do not appear to work in general for fluid loaded targets. In particular, flexural resonances are predicted below coincidence frequency where they should not be observed. Further, the lowest symmetric modes are over-estimated when compared to the exact theory predictions. In addition, the presence of water borne waves is not observed from thin shell theories while they are present in exact calculations. Our interest is to develop a thin shell theory that can account for all of the above features correctly and thus can be used as a better approximate theory for future work. We thus construct shell theories which include the various shell features without undue approximation. We include the usual kinetic energy terms, contributions from a generalized Hooke's law, and rotary inertia terms. We then include a complex impedance (not the usual real component). This construction allows us to approximate the exact results in greater detail than earlier theories for three dimensional scatterers. Detailed comparative numerical examples are presented.