The impression creep of a power-law material by pushing a rigid cylindrical punch into an existing cavity of the same diameter as the punch located in the surface of a half-space was studied by using finite element method. For both the slip and stick conditions at the interface of the punch and the half-space, there is a well-defined steady punch penetration velocity after a transient stage. The steady penetration velocity is a power function of the applied load, which has the same stress exponent as by conventional creep tests. It increases with the stress exponent but decreases with increasing cavity depth, and is the largest for all slip condition and the smallest for both stick condition on the circular interface between the punch and the cavity and all stick condition.