The need for a computationally efficient yet physically realistic water model for molecular simulation is longstanding. To account for intermolecular interactions with other molecules, for example the hydration of biomolecules, the model has to be able to adapt itself to different environments. To this end, a number of water models have been proposed that incorporate polarizability with varying degrees of success. We have developed new water models, flexible as well as rigid, on the basis of the shell concept, with three atoms and an extra particle representing the electronic degrees of freedom. This particle is coupled to a dummy position on the bisector of the molecule by a harmonic spring. We named the models SW, or shell water models. To account for anisotropic polarization, the spring force on the shell particle has been modified to depend on the displacement of the shell particle in the molecular coordinate frame. The model is constructed so as to reproduce the vacuum dipole and quadrupole, and the spring constants are chosen such that the polarizability, be it isotropic or anisotropic, is consistent with experimental data. Then the Lennard-Jones parameters are optimized to reproduce the liquid energy and density. The model is evaluated by checking liquid-and gas-phase properties, and the influences of anisotropy and flexibility are discussed.