In this talk, we discuss the propagation of surface waves in an isotropic half space modelled with the linear Cosserat theory of isotropic elastic materials. To this aim the method based on the algebraic analysis of the surface impedance matrix and the algebraic Riccati equation has been employed. Moreover, this method allows to prove the existence and uniqueness of a subsonic solution of the secular equation, a problem that remains unsolved in almost all generalized linear theories of elastic materials. Explicit numerical calculations are made for aluminum-epoxy in the context of the Cosserat model. Furthermore, the novel form of the secular equation for isotropic elastic material which has not been explicitly derived elsewhere will also be discussed.