We develop numerical solutions of a theoretical model which has been proposed to explain the formation of subglacial bedforms. The model has been shown to have the capability of producing bedforms in two dimensions, when they may be interpreted as ribbed moraine. However, these investigations have left unanswered the question of whether the theory is capable of producing fully three-dimensional bedforms such as drumlins. We show that, while the three-dimensional calculations show realistic quasi-three-dimensional features such as dislocations in the ribbing pattern, they do not produce genuine three-dimensional drumlins. We suggest that this inadequacy is due to the treatment of subglacial drainage in the theory as a passive variable, and thus that the three-dimensional forms may be associated with conditions of sufficient sub-glacial water flux.