In a Cerenkov FEL (CFEL), the phase velocity of an EM wave is determined by geometry (i.e., waveguide radius and inner liner radius) and by material parameters (i.e., the dielectric constant of the liner). Changes or fluctuations in any of these parameters induce changes (or fluctuations) in the phase velocity of the EM wave and thus can degrade the gain of the CFEL. To investigate the effect of such fluctuations on the gain, a method is developed to describe the effect of a slowly varying inner liner radius on the EM wave propagation and consequently on the gain of the CFEL. As an example, results for a low gain, 800 mA Cerenkov FEL operating at a frequency of 50 GHz and a maximum beam voltage of 100 kV are presented.