The accurate reproduction of the hysteretic behaviour exhibited by soils under cyclic loading is a crucial aspect of dynamic finite element analyses and is typically described using the concept of damping ratio. In this paper, a general algorithm is presented for assessing the damping ratio simulated by any constitutive model based on the registered behaviour in three-dimensional stress-strain space. A cyclic nonlinear elastic model capable of accurately reproducing a wide range of features of soil behaviour, including the variation of damping ratio with deformation level, is chosen to illustrate the capabilities of the proposed algorithm. The constitutive model is described and subsequently employed in two sets of finite element analyses, one involving the dynamic response of a sand deposit subjected to different types of motion and another focussing on the simulation of a footing subjected to cyclic vertical loading. The application of the presented algorithm provides insight into the processes through which energy is dissipated through hysteresis.