Jupiter’s icy moon Europa displays a variety of lineament types ranging from arcuate to “wavy” to cycloidal. These features can span 100s of km and reach heights of ~200 m. Here we explore how these features could evolve in a rotating diurnal stress field, with contributions from nonsynchronous rotation (NSR) and obliquity stresses. Previous work has invoked simulations of diurnal and added obliquity stress to explain Europa’s observed cycloidal lineaments. However, these models assumed an elastic ice shell, and neither of these two stress mechanisms alone can simulate Europa’s wavy lineaments. We expand on that previous elastic-shell modeling to demonstrate that diurnal tidal stresses can combine with NSR and obliquity stresses to create cycloidal lineaments or lineaments with a “wavy” planform, as simulated with the viscoelastic model SatStressGUI. If only diurnal tidal stress, or obliquity plus diurnal tidal stresses, are considered, then cycloidal lineaments are formed in response the changing magnitude and direction of the resultant principal stresses. The characteristics of the lineaments are controlled by a variety of parameters mainly propagation speed, ~1–5 m/s, thickness and viscosity of the lower ice layer, with a thicker and more viscous lower ice resulting in a smaller stress magnitude. For NSR, the magnitude of the simulated stress is chiefly dependent on the period of NSR and thickness and viscosity of the upper ice layer, such that a longer NSR period or a thicker ice shell with a low viscosity results in a smaller stress magnitude. When NSR stress is added and is similar in magnitude to the diurnal or obliquity stress, the simulated propagating lineaments can be wavy in planform shape. As the magnitude of the NSR stress is increased such that NSR stress dominates over diurnal and obliquity stress, the simulated lineaments are generally arcuate. We suggest that small amounts of NSR stress might have contributed to the formation of cycloids but that significant NSR was not necessary to account for their planform shape. But NSR may be an important contributing factor to the formation of the Europa’s wavy lineaments.