The excitation of maser emission in millimeter and submillimeter transitions of interstellar and circumstellar water is considered. An escape probability method is used to determine the equilibrium populations in 349 rotational states of both ortho- and para-water under varying conditions of gas temperature, density, water abundance, and radiation field. It is shown that, under those conditions believed to prevail around late-type stars and within star-forming regions, strong millimeter and submillimeter water maser emission can be generated by collisional excitations by H2. Several maser transitions can have strengths close to that of the 22 GHz line. The water maser line which can be observed from mountaintop facilities and those which will require air- or space-borne platforms are indicated. The exact portion of parameter space in which each maser transition exhibits peak emission is shown.