The spin ice materials Ho2Ti2O7 and Dy2Ti2O7 are experimental and theoretical exemplars of highly frustrated magnetic materials. However, the effects of applied uniaxial pressure are not well studied, and here we report magnetization measurements of Ho2Ti2O7 under uniaxial pressure applied in the [001], [111], and [110] crystalline directions. The basic features are captured by an extension of the dipolar spin ice model. We find a good match between our model and measurements with pressures applied along two of the three directions, and we extend the framework to discuss the influence of crystal misalignment for the third direction. The parameters determined from the magnetization measurements reproduce neutron scattering measurements that we perform under uniaxial pressure applied along the [110] crystalline direction. In the detailed analysis, we include the recently verified susceptibility dependence of the demagnetizing factor. Our work demonstrates the application of a moderate applied pressure to modify the magnetic interaction parameters. The knowledge can be used to predict critical pressures needed to induce new phases and transitions in frustrated materials, and in the case of Ho2Ti2O7 we expect a transition to a ferromagnetic ground state for uniaxial pressures above 3.3 GPa.