Theoretical models for water jet cutting, continuous water jet penetration, and pulsed water jet penetration of materials were developed, and applied to existing data. Control volume analyses of jet penetration and jet cutting, coupled with the rheological model of a Bingham plastic, were used to develop and solve the model equations in closed form. For pulsed water jet penetration, a periodic forcing function was defined and applied to the developed differential equation for closed form solution. Evaluation of coefficient parameters (coefficient of friction $C\sb{f}$, coefficient of damping $\varsigma$, and duration of impulse pressure $t\sb{i}$ for pulsed jet penetration) contained in the models was done by trial and error application of the theoretical equations to each relevant data set. Discontinuities in the data, plotted as dimensionless depth of penetration $Z/D\sb{n}$ versus exposure time t, affected the degree of fit of the theoretical models to the data, but overall, good prediction of the data trends was obtained. Values of the coefficient parameters for water jet penetration or cutting of oil sands were found to be of similar magnitude for a variety of jet pressures and nozzle diameters; but for higher strength substances, such as granite, the values of the coefficient parameters were found to vary significantly. The theory behaved well with full dynamic pressure of the jet $P\sb{d}$ as the impulse pressure--instead of the water hammer pressure--and 1/10 $P\sb{d}$ as the reduced pressure for the continuous portion of the water jet. Unlike the theoretical models of other researchers, the models developed in this work distinguished between the separate cases of water jet penetration (where the nozzle remains fixed relative to the material) and water jet cutting (where the nozzle is traversed relative to the material). (Abstract shortened by UMI.)