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A dielectric rod enveloped in gaseous plasma can act as a supporting structure for electromagnetic surface waves. The dielectric constant of the plasma and hence the electron number density in the vicinity of the rod may be determined from measurements of the phase-change coefficient of the EH11 mode supported by the plasma-clad rod. Measurements of radial density distribution have been carried out in an unmagnetised argon afterglow plasma at 35Gc/s and compared with double-probe measurements.