Solids can fail when subjected to repeated deformations or stresses. Failure is not observed below a fatigue limit, whereas
above, the the number of cycles, or time, to failure is a strong function of the deformation/stress amplitude. We perform computer simulations of a model glass subjected to cyclic shear deformation, to investigate fatigue failure. The failure times diverge as a power law as the cyclic shear yielding point is approached from above, with strong dependence of the degree of annealing. The dissipated work during the cycles of before failure have a striking relationship to the failure times. These results, along with attempts to rationalise them, are presented.