This work deals with the study of the viscoelastic and adherence properties of pressure-sensitive adhesive (PSA) formulations dedicated to medical applications. We have developed a specific viscoelastic substrate to measure the adherence properties of PSAs that mimics adhesion on human skin. In the present article, we describe several experiments dedicated to a better understanding of adhesion on viscoelastic substrates without discussing specifically the case of human skin. In this way, we have studied different model adhesive formulations based on real medical formulations, and we have related the rheological behavior to the adherence properties obtained on different substrates to study the various specific effects due to the viscoelasticity of soft substrates. We propose from this study a failure criterion that allows one to derive a reasonable estimate of the peeling transition rate from cohesive to interfacial or stick-slip failure.