In this short paper we study the counterpart, within the context of a general class of fluids, of two famous unsteady flows originally studied by Stokes, within the context of Navier–Stokes fluid, namely Stokes’ first and second problems. The class of fluids considered, stress power-law fluids, are capable of stress thinning or stress thickening and can describe phenomena that the classical power-law fluids are incapable of modeling. Within the context of the problems considered, we are able to find solutions wherein stress boundary layers develop.