We have extracted stress-strain field (SSF) gradient and divergence representations from nanoindentation data sets of bulk solids often used as thin film substrates: bearing and tooling steels, silicon, glasses, and fused silica. Oscillations of the stress-strain field gradient and divergence induced in the subsurface layer by the nanoindentation have been revealed. The oscillations are especially prominent in single indentation tests at shallow penetration depths,