This paper discusses the effects of couple-stresses in linear elasticity, focusing on the Cosserat equations and their linearized forms. The theory, developed by Voigt and the Cosserats, accounts for couple-stresses in addition to forces. The paper presents solutions for wave propagation, vibration, stress concentration, and strain nuclei within a linearized couple-stress theory for perfectly elastic, centrosymmetric-isotropic materials. TRUESDELL and TOUPIN derived the Cosserat equations, while TOUPIN later derived constitutive equations for finite deformation. Upon linearization, TOUPIN's equations match those of AERO and KUVSHINSKI. However, GRIOLI's linearized equations differ from TOUPIN's. The discrepancy arises from different derivation methods, and the paper reviews both derivations to identify the point of divergence. The paper discusses the uniqueness of solutions for linear equations, based on the positive definiteness of internal energy-density. Although no proof is given, the paper provides justification and an example of failure of uniqueness when energy-density is not positive-definite. It shows that five boundary conditions are sufficient for uniqueness, similar to the classical theory of thin plates. In the linear theory, an additional modulus of elasticity is introduced, with dimensions of force. The square root of the ratio of this modulus to the shear modulus has dimensions of length, l, a material property that affects equations with and without couple-stresses. The paper suggests that l is small compared to typical dimensions and wavelengths, but its influence may become significant at smaller scales. Plane wave propagation is analyzed, showing a non-dispersive dilatational wave and two rotational waves, one propagating and one non-propagating. The propagating rotational wave's group velocity increases with wave number and l. The non-propagating wave produces a boundary layer effect. The displacement equations are reduced to Lamé's equations, with modified rotation potential equations. In steady vibration, the rotation equation separates into two Helmholtz equations. The paper also presents solutions for thickness-shear vibrations of an infinite plate, showing natural frequencies exceeding the integral.This paper discusses the effects of couple-stresses in linear elasticity, focusing on the Cosserat equations and their linearized forms. The theory, developed by Voigt and the Cosserats, accounts for couple-stresses in addition to forces. The paper presents solutions for wave propagation, vibration, stress concentration, and strain nuclei within a linearized couple-stress theory for perfectly elastic, centrosymmetric-isotropic materials. TRUESDELL and TOUPIN derived the Cosserat equations, while TOUPIN later derived constitutive equations for finite deformation. Upon linearization, TOUPIN's equations match those of AERO and KUVSHINSKI. However, GRIOLI's linearized equations differ from TOUPIN's. The discrepancy arises from different derivation methods, and the paper reviews both derivations to identify the point of divergence. The paper discusses the uniqueness of solutions for linear equations, based on the positive definiteness of internal energy-density. Although no proof is given, the paper provides justification and an example of failure of uniqueness when energy-density is not positive-definite. It shows that five boundary conditions are sufficient for uniqueness, similar to the classical theory of thin plates. In the linear theory, an additional modulus of elasticity is introduced, with dimensions of force. The square root of the ratio of this modulus to the shear modulus has dimensions of length, l, a material property that affects equations with and without couple-stresses. The paper suggests that l is small compared to typical dimensions and wavelengths, but its influence may become significant at smaller scales. Plane wave propagation is analyzed, showing a non-dispersive dilatational wave and two rotational waves, one propagating and one non-propagating. The propagating rotational wave's group velocity increases with wave number and l. The non-propagating wave produces a boundary layer effect. The displacement equations are reduced to Lamé's equations, with modified rotation potential equations. In steady vibration, the rotation equation separates into two Helmholtz equations. The paper also presents solutions for thickness-shear vibrations of an infinite plate, showing natural frequencies exceeding the integral.