To ensure model stability, the momentum balance, constitutive law, and hardening law must all be considered. In addition to a constitutive law that dissipates energy during all deformations, stability requires that infinitesimal perturbations to the model solutions decay. Their growth would imply that solutions are sensitive to small changes in initial conditions. Perturbation equations are introduced, linearized, and solved using normal modes. If a mode can grow, it can generate spurious motions from small initial perturbations. This stability analysis improves our understanding of the behavior of an isotropic viscous-plastic model. The analysis shows that it has unstable opening and closing deformation states.