A system of three-variable differential equations, which has a nonstationary trajectory transition through the control of a single rate parameter, is formulated. For the nondimensional system, the critical trajectory creeps before a transition in a long-lasting plateau region in which the velocity vector of the system hardly changes and then diverges positively or negatively in finite time. The mathematical model well represents the compressive viscoelasticity of a spring-damper structure simulated by the multibody dynamics analysis. In the simulation, the post-transition behaviors realize a tangent stiffness of the self-contacted structure that is polarized after transition. The mathematical model is reduced not only to concisely express the abnormal compression problem, but also to elucidate the intrinsic mechanism of creep-to-transition trajectories in a general system.