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This paper explains the wrinkling behavior of a bilayer system comprised of a soft, thick hydrogel on a hard thin skin in which the hydrogel has viscoelastic properties. The role of external stress and viscoelastic properties on the morphology of nanoscale wrinkles is discussed in a time-dependent mechanical and thermomechanical framework and compared with the corresponding results from a linear elastic treatment of the hydrogel. Our results show that the strain rate and magnitude of strain have substantial impact on nanoscale wrinkle morphology when viscoelasticity of the substrate is included in the model. As such, engineering the relaxation time through the material synthesis process or material selection plays an important role. This is important to modeling an autoregulatory humidity sensing device that was previously developed by our group and others, where the formation of humidity-dependent nanoscale wrinkles tunes the transmission or scattering of light through the substrate, thereby enabling a plasmonic nanoparticle array to switch on or off plasmonic heating of the system that generates or removes the nanoscale wrinkles. Three different lumped viscoelastic models are applied: generalized Maxwell (GM), generalized Kelvin–Voigt (GK), and Burger (BR) models. Time evolution analysis of these models, including comparison with the validated linear elastic model at high relaxation time and with experimental data, shows best agreement with the GK result. Finally, we quantitatively demonstrate how the morphology of nanoscale wrinkles that is accessible to viscoelastic models can adjust the light transmission across the substrate by amounts that are useful for the autoregulatory device. This viscoelastic modeling will enable more quantitative predictions and design principles for taking advantage of responsive materials such as for pressure or humidity sensors or thermal-responsive drug delivery systems. [ABSTRACT FROM AUTHOR]