For the time integration solution of the impulsive dynamic contact problem of high-speed rotating disks formulated by the finite element technique, the velocity and acceleration contact constraints as well as the displacement contact constraint are imposed for the numerical stability without spurious oscillations. The solution of the present technique is checked by the numerical simulation using the concentric high-speed rotating disks with the clearance and impulsive loading. It is shown that the almost steady state solution agrees with the corresponding analytical solution of the elasticity and that the differentiated constraints are crucial for the numerical stability of such high-speed contact problems of the disks under impulsive loading.