A method for calculating the eigenwaves in a “semi-infinite” uniaxial dielectric medium (UDM) is proposed. The term “semi-infinite” medium implies the presence of at least one flat boundary of such medium. This method allowed writing out all the components of the total fields in UDM. With the help of that analytical representation of the fields, the problem of the propagation of Dyakonov surface waves guided by the planar interface of two identical UDM with their optic axes lying in the interface plane was investigated to derive an exact analytical expression for the phase speed, when the direction of propagation bisects the angle formed by the two optic axes. On the basis of the solutions found, the energy characteristics were studied, which demonstrated the presence of the flux of average over a period power of the Dyakonov wave along the coordinate axes lying in the plane of UDM boundary. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.