A theoretical model of a stationary low-pressure gas discharge sustain
ed by the surface type X-mode (STXM) in a planar metal waveguide with
a dielectric coating is presented. The STXM are eigenmodes of this dis
charge structure, they possess eigenfrequencies in the range between t
he second and the third electron cyclotron harmonic, propagate across
an external steady magnetic field oriented parallel to the plasma-diel
ectric interface. The problem is studied using a kinetic description f
or plasma particles motion and model of their diffuse reflection from
the dielectric interface. The spatial distributions of the sustained p
lasma and the STXM electromagnetic fields, as well as the effect of ex
ternal magnetic field and electrodynamic characteristics of the discha
rge chamber on the discharge parameters are studied analytically.