Slow, nondissociative, magnetohydrodynamic shock waves that propagate in dense molecular gas are a probable source of water maser emission in regions of active star formation. We have constructed a model to compute the water maser emission expected from such shocks. We have integrated a set of one-dimensional hydrodynamics equations in which the neutral species and charged particles are treated separately as two interpenetrating but weakly coupled fluids, and then solved the equations of statistical equilibrium to obtain the level populations of the lowest 179 and 170 rotational states of ortho- and para-H2O. Our model includes radiative cooling due to rovibrational transitions of H2O, CO and H-2, and cooling due to dissociation of H-2 and due to gas-grain collisions. The fractional ionization is extremely low in the dense shocks considered here and resides primarily on charged dust grains. We find that luminous H2O maser emission is expected from dense nondissociative MHD shocks: in particular, the warm molecular gas behind such shocks is ideal for pumping numerous low- and high-lying submillimeter maser transitions. Here we present results for shocks with initial H-2 densities of 10(7)-10(9.5) cm(-3) and velocities of propagation up to similar to 45 km s(-1). Over this entire parameter space, we have determined the efficiency with which shock energy is converted into maser luminosity for each of the water maser transitions that have so far been observed in interstellar gas, under conditions where the maser action is saturated, and we have considered the geometrical effects which determine whether or not a given maser transition will be saturated. For the range of preshock densities that we considered, nondissociative shocks give rise to individual masing regions with sizes of similar to 10(12) to a few times 10(14) cm, and, given suitable geometries, can reproduce the high brightness temperatures characteristic of observed maser sources. Nondissociative shock models are also successful in accounting for the magnetic field strengths that have been inferred from observations of Zeeman splitting. Maser line ratios are presented for use as potential probes of the conditions in the masing gas. These are compared with observational data, some of which cannot be explained on the basis of fast dissociative shock models.
