This paper is concerned with stresses in metal cutting in the tool itself. These stresses are within the elastic region and can therefore be treated by the methods of the theory of elasticity. The tool is considered as a wedge having normal and tangential loading on one face. Equations for the stress components at any point of the tool tip are obtained. Particular attention is given to the edge of the tool where stresses of several hundred thousand pounds per square inch are found. The calculations offer a basis for the rational design of cutting tools and they also should be of value in metal-cutting research on tool failure.