Slow penetration rate is a major factor in the high cost of deep drilling operations worldwide. A contributing factor is the excessive energy required to create and transport rock cuttings under high confining pressure. This work describes a new analytical single cutter model of cutting rock under confining pressure that was adapted from a model of machining metal. The original model quantifies an increase in shear plane area resulting from an increase in friction on the cutter face and/or in back rake angle based on the principle of minimum energy. An adaptation of the model accounts for the effects of the confined shear strength of the rock and confining pressure-induced friction on the shear plane. Additional model terms were developed to account for the effect of specific dysfunctions, i.e. cutter balling and severe "global" balling. The model predicts distinctive characteristics of each condition: no dysfunction, cutter balling, and global balling in addition to unique changes in these characteristics as a function of confining pressure. The relevance of model predictions is supported by comparison to single cutter test results on shales.