Continuous-time models for high-cycle fatigue are useful for arbitrary load histories with nonproportional or aperiodic load. In this work, we consider a previously published model (Ottosen etal. 2008, Ottosen et al. 2018), which is based on an endurance surface controlled by the currentstress state and a load history-dependent back-stress, where the latter controls the center of the endurance surface. Damage develops when this endurance surface moves, but only during the loadingphases. The versatility of the model comes at a computational cost; it is necessary to integrate theback-stress evolution and damage across the full load history. We seek a method for acceleratingthe computations in the special case of cyclic load.We fit the continuous-time fatigue model to the material data of AISI 4340 alloy steel by consideringthe Haigh diagram and the Wöhler curve. There is compelling experimental evidence that rotarystress states are more detrimental to materials than proportional states (Anes et al. 2014). To capture this effect, a nonproportional load case must be included in the fitting procedure. Due to thelack of experimental work on nonproportional load for AISI 4340, we fit the model parameters to aqualitatively proper model behavior.We investigate the development of a steady-state in the incremental damage per cycle for proportional and nonproportional cyclic load, respectively. The existence of a steady-state would enableextrapolation of the damage at the end of the transient, thus reducing the number of cycles necessary for integration. We demonstrate that proportional stress states lead to a brief transient of lessthan ten cycles, whereas some cases of nonproportional stress states lead to a prolonged transientthat persists over several hundred cycles.Having established the existence of a steady-state, we formulate a method of extrapolation. Thedamage Di at the end of each cycle i is obtained by integration, producing a sequence Sn = {Di}ni=0with D0 = 0, and n the total number of integrated cycles. Linear extrapolation is employed foreach pair (Di−1, Di) to find the extrapolated damage D˜ Niat cycle N ≫ n. Thus, we obtain anew sequence S˜n = {D˜ Ni}ni=1 of extrapolated values. Finally, an approximation of the damageDN is obtained by applying the sequence acceleration method known as Wynn’s epsilon algorithm(Wynn 1956) to S˜n. We show that this procedure efficiently reduces the computational cost for thecontinuous-time fatigue model for general cyclic load.