The intrusive and host rocks of epizonal igneous intrusions cooled by groundwater convection are depleted in 18O by oxygen exchange with low-18O meteoric waters. This study describes numerical experiments on the hydrothermal convective cooling and 18O depletion of a family of simple two-dimensional model intrusions. Cooling and depletion histories are calculated on the basis of conservation laws for mass, Thermal energy, and 18O atoms along with Darcy's law to describe flow in permeable rock and a kinetic description of water-rock oxygen exchange. Exchange is described on the basis of the measured oxygen diffusivity in feldspar which is large compared to that in the other rock-forming minerals. The resulting equations are solved using finite difference approximations. The numerical experiments examine the effect of intrusion size, intrusive and host rock permeabilities, and host rock thermal environment on the 18O depletion that develops as an intrusion cools and show that the depletion patterns in a cooled intrusion are sensitive to parameters describing the intrusion and its environment. The dependence of several general characteristics of these patterns on the model parameters is described. Depletions obtained from the sampling of natural intrusions are discussed in the context of this sample family of models.