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A computational model for determination of service life of gears in regardto bending fatigue in a gear tooth root is presented. The Coffin-Manson relationship isused to determine the number of stress cycles Ni required for the fatigue crackinitiation, where it is assumed that the initial crack is located at the point of the largeststresses in a gear tooth root. The simple Paris equation is then used for the furthersimulation of the fatigue crack growth, where required material parameters have beendetermined previously by the appropriate test specimens. The functional relationshipbetween the stress intensity factor and crack length K=f(a), which is needed fordetermination of the required number of loading cycles Np for a crack propagation fromthe initial to the critical length, is obtained numerically in the framework of the FiniteElement Method. The total number of stress cycles N for the final failure to occur isthen a sum N = Ni +Np.