Our daily lives are constantly surrounded by dynamic stimuli, and our skin is deformed in a time-dependent manner. Although skin plays an important role in transmitting stimuli received at the surface to mechanoreceptors, few studies have investigated how differences in skin viscoelasticity affect the mechanical stimuli propagation in the skin. Therefore, using a finite element model, we evaluated the effects and trends of changes in the stiffness and viscoelasticity of the skin on the propagation of mechanical quantities between skin layers where mechanoreceptors are present when subjected to periodic stimuli. First, we constructed a new, sophisticated mathematical model of skin viscoelasticity based on the history-dependent deformation behavior of human skin obtained experimentally. We were able to construct a skin model that thoroughly reproduced the actual human skin deformation behavior at oscillations as fast as 10 Hz by setting viscoelastic parameters with a short time constant (0.001–0.006 s). Then, we calculated how skin material parameters affect the propagation of the mechanical quantities in the skin during the history-dependent skin deformation response to periodic stimuli. The finite element analysis showed that not only stiffness but also viscoelasticity markedly affected the mechanical stimuli propagation in the skin, and the effect differed depending on the layer. In particular, greater immediate responsiveness of the dermis contributed to greater propagation of the mechanical stimulus. Our results indicate that more attention needs to be given to the differences in the time-dependent intradermal mechanical stimuli propagation caused by individual's skin viscoelasticity.