A theory for the growth of cracks by fatigue is developed that is analogous to the brittle fracture of high strength materials. It is argued that it is possible to describe crack growth with a curve of resistance which is dependent on the alternating stress at low rates of crack propagation. At higher rates there is much less dependency on the alternating stress. Once such curves have been prepared the rate of crack growth can be found from the value of the crack driving force. This force is dependent mainly on the maximum stress and crack length.