By means of integral‐transform techniques, the problem of steady motion and simultaneous harmonic oscillation of a smooth flat indenter is formulated and solved. The boundaries of the indenter are assumed to be fixed with respect to a coordinate system moving with steady velocity. A low‐frequency approximation for this case is obtained. The results of the approximation are subsequently used with a method of Crozier and Hunter to obtain the magnitude of the changing boundary when a curved or wedge indenter is considered.