It is shown that some of the assumptions and further restrictions imposed in Reference (Muki and Sternberg in Z. Angew. Math. Phys. 16:611–648, 1965) in relation to development of the plane strain version of the conventional couple-stress theory are invalid. This finding comes a result a new development presented in the first part of this study (Soldatos in J. Elast. 153:185–206, 2023), according to which a refined couple-stress theory of isotropic linear elasticity enables determination of the trace of the couple-stress tensor and, henceforth, of the antisymmetric part of the stress and, thus, the total stress tensors. The present communication reconsiders those assumptions and restrictions (Muki and Sternberg in Z. Angew. Math. Phys. 16:611–648, 1965), separates the ones that are still valid from their invalid counterpart, and, to the extent that this is possible and acceptable, rebuilds the foundation that the plane strain concept can be based upon in polar isotropic linear elasticity. It is accordingly found, and also demonstrated with a couple of relevant boundary value problem applications, that, while the assumption of plane strain naturally guarantees that displacements and strains depend only on in-plane co-ordinates parameters, the couple-stress and the stress tensors generally depend on the out-of-plane co-ordinate parameter as well.
