The diffusion problem in the impression creep of a thin film by a cylindrical punch is analyzed. It is found that at low stresses the impression velocity is proportional to the punching stress. For the same punching stress and the same punch radius the impression velocity decreases for a rigid substrate, and increases without the substrate as the thickness of film decreases. Two limiting cases for the rigid substrate agree with the previous work, namely, the impression velocity is inversely proportional to the punch radius for impression creep of a half‐space, and inversely proportional to the square of the punch radius for impression creep of a thin film. Without the substrate the impression velocity for impression creep of a thin film is inversely proportional to the thickness of the film and independent of the punch radius.