The apparent paradox of two theories of fracture depending on whether the applied load is tensile or compressive is resolved. Although in compression, fracture seems to occur when the maximum tensile stress around a hole reaches a critical value it is suggested that fracture occurs when the crack extension force at the tip of a microcrack in the neighbourhood of the crack tip reaches a critical value. An essential difference in behaviour under tension and compression is that whereas in tension the crack extension force increases with crack growth, in compression a maximum value of the crack extension force is reached with further crack growth causing a decrease in its value. If the defects, which must exist at the edge of a machined hole, are small, then the crack extension force is controlled by the maximum tensile stress at the surface of the hole. The degree of smallness is different for tension and compression. In tension, the defects must be less than one fifth of the root radius of the tip of the hole and if the hole is sharp enough, the defects will be larger than this value and the crack extension force will be given by the usual fracture mechanics expressionG = σ2 πc/E. In compression the defects must, in the limiting case, be greater than the root radius of the tip of the hole (in a more typical case, greater than twice the root radius) if the crack extension force is not to be controlled by the maximum tensile force. Such large defects are impossible since the sharpness of the root radius is limited by the defect size and thus in compression, fracture from machined notches will always be controlled by the maximum tensile stress.