The eikonal equation links wave optics to ray optics. In the present work, we show that the eikonal equation is also valid for an approximate description of the phase of vector fields describing guided-wave propagation in inhomogeneous waveguide structures in the adiabatic approximation. The main result of the work was obtained using the model of adiabatic waveguide modes. Highly analytical solution procedure makes it possible to obtain symbolic or symbolic-numerical expressions for vector fields of guided modes. Making use of advanced computer algebra systems, we describe fundamental properties of adiabatic modes in symbolic form. Numerical results are also obtained by means of computer algebra systems. © 2020, Springer Nature Switzerland AG.