Plastic and creep deformations around a crack front and in the wake of a moving crack under cyclic loading are implemented into the life-prediction code, FASTRAN (a strip-yield model). Creep deformations are modeled by stress relaxation around the crack-tip location, since the crack-front material is under displacement control due to the surrounding elastic material. Sinusoidal and trapezoidal loading are considered. A modified linear superposition model was used to compute the cyclic- and time-dependent damage, which was based on the stress-intensity-factor concept for creep-brittle materials. Application of the modified strip-yield model was made on two sets of test data on Inconel-718 alloy. The environments were laboratory air or helium gas. From the literature, the “environment” had been shown to be a major contributor to damage magnitudes. Thus, the time-dependent crack-growth constants were selected to match the test data. In addition, the effects of a small overload on time-dependent damage, and the effects of stress relaxation and varying temperatures on crack-opening stresses and cyclic crack-tip-opening displacements, were studied.