In a shrink-fitted joint, the interface pressure plays an important role as it is the main source of the joint and it keeps the joining components together. However, time-variation of the interface pressure causes parametric instability in the system. In this paper, the effect of time-variant interface pressure on the dynamics of two shrink-fitted rings has been studied. Deriving a dynamic equation of motion of the joint of two shrink-fitted rings and substituting time-variant interface pressure in the equation, the problem extends to nonlinear vibration. The obtained equation of motion, which contains parametrically excited terms, is a general form of Mathieu’s equation. A perturbation method, to determine the instability regions of motion, is applied to obtain the transition curves. To validate the obtained stability regions, an experiment has been performed. Both the analytical and experimental results demonstrate that by increasing the value of the interface pressure, the natural frequencies of the joint increase.