This paper describes a finite-element analysis of surface microwaves coupled to a cold nonmagnetized plasma for chemical vapor deposition (CVD). The microwave-plasma coupling is taken into account by introducing the frequency-dependent permittivity. The computed resonant modes of the surface wave on the interface between the dielectric and plasma in a cylindrical vessel are shown to be in good agreement with the theoretical ones. Moreover, the computed field distribution for a waveguide loaded cylindrical vessel agrees well with that computed by the finite-difference time-domain (FDTD) method.