The magnetically frustrated spin ice family of materials is host to numerous exotic phenomena such as magnetic monopole excitations and macroscopic residual entropy extending to low temperature. A finite-temperature ordering transition in the absence of applied fields has not been experimentally observed in the classical spin ice materials Dy2Ti2O7 and Ho2Ti2O7. Such a transition could be induced by the application of pressure, and in this work we consider the effects of uniaxial pressure on classical spin ice systems. Theoretically, we find that the pressure-induced ordering transition in Dy2Ti2O7 is strongly affected by the dipolar interaction. We also report measurements of the neutron structure factor of Ho2Ti2O7 under pressure and compare the experimental results to the predictions of our theoretical model.