The propagation of two orthogonally polarized coaxial light beams in plannar waveguides is studied by variational approach as well as numerical method. The condition for soliton-like mutually-trapped propagation of the two beams is obtained. We analysed the different characteristics of mutually-trapped propagation in two cases with or without linear birefringence. We find that there is an essential difference between mutually-trapping beams and the rigorous vector spatial soliton.