Oblique indentation of power law creeping solids at plane strain conditions is examined with rigid-perfectly plastic material behaviour emerging as an asymptotic case. Indenter profiles are dealt with in general circumstances and represented by homogeneous functions. The core of the method developed draws on self-similarity and is based on an intermediate flat die solution. By this approach the problem of a moving contact boundary may be suppressed and the ensuing procedure becomes independent of loading, geometry, history and time. A computational method, based on the reduced procedure, is developed to obtain high accuracy solutions based on finite elements and applicable to non-linear elasticity. The originally stated problem is then solved subsequently by simple cumulative superposition and results given as a function of impression depth. The relation between contact depth and area is found to be invariant and only dependent on the power law exponent, the amount of friction, the profile and the angle of inclination of the indenter. Detailed results are given for local states of stress and deformation for flat and cylindrical dies at variation of the remaining three stated parameters. The presence of local stick and slip is given due attention and global relations between loading and indentation depth and contact area discussed for practical applications. The fundamental framework laid down may be applied to structural assemblies, joints and seals and diverse applications as flattening of rough surfaces, compaction of powder aggregates and ice-offshore structure interaction.