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.