<p>In this paper, a distinct numerical approach to simulating cyclic loading in geotechnical structures is introduced. The method, to date mostly used in non-geotechnical applications, is often referred to as accelerated cyclic loading, the skipped cycles or the jump-cycle method. In geotechnical engineering, there are, in general, distinguished two approaches to numerical simulations of cyclic strain accumulation: implicit and explicit methods. The implicit approach models each cycle in its entirety, while the explicit approach focuses only on the average values of each cycle. Due to the computational intensity, simulating thousands of cycles with the implicit method is often practically impossible, making the explicit approach the only alternative. An alternative approach to cyclic loading simulations is introduced in this paper, which can be applied in combination with any implicit cyclic constitutive model and is denoted here as the accelerated implicit cyclic method. The method, ideally, yields results identical to the implicit method with computational efficiency of the explicit method. The method is presented first and its accuracy with regards to the fully implicit simulation is demonstrated by finite element simulations of elements test and an example model of a laterally loaded pile. The most simple version of this method with a linear extrapolation based on one implicit loading cycle is adopted, which can be, however, easily modified for more complex extrapolations in future works. Simulations are performed with a hypoplastic constitutive model for sand.</p>