We present the results of a theoretical study investigating the effects of photoionization and heating by X‐rays on discs around low‐mass stars. In particular, we address the question of whether or not X‐rays can drive a disc wind. First, we construct a one‐dimensional ‘quasi‐hydrostatic’ model, which solves for the vertical structure introduced by X‐ray heating. We consider uniform X‐ray illumination of the disc, but the X‐ray fluxes required to heat the disc significantly are much greater than those seen by recent observations. When the model is extended to consider heating from a central X‐ray source, we find that the one‐dimensional model is only valid very close to the star. We extend our analysis to consider a simple two‐dimensional model, treating the disc as a two‐layered structure and solving for its density profile self‐consistently. For T Tauri stars, we are able to set a crude upper limit on the mass‐loss rate that can be driven by X‐ray photoevaporation, with a value of ≃10−13 g cm‐2 s−1. Our model is designed to maximize this value, and most likely overestimates it significantly. However, we still find a mass‐loss rate which is less than that found in studies of ultraviolet photoevaporation. We conclude that in the presence of a significant ultraviolet field, X‐ray driven disc winds are unlikely to play a significant role in the evolution of discs around low‐mass stars.