Effects of electron mass on Alfven waves in a cylindrical, inhomogeneous plasma are examined, in the cold plasma approximation, and in the frequency range from well below to several times the ion cyclotron frequency, omega ci. Both propagating (kz2>0) and axially evanescent (kz2<0) modes are considered. It is shown how the cold plasma modes are coupled by a density gradient and how these modes are connected across the four domains bounded by kz2=0 and omega = omega ci. Low-frequency surface-wave modes, predicted for a density step profile, lose their identity in a diffuse profile and merge with a discrete set of shear wave modes. High frequency surface modes survive in a diffuse profile. These, and other high frequency fast waves modes are axially evanescent at frequencies below the kz=0 cut-off frequency, and are Alfven-resonant in the cut-off frequency is above the ion cyclotron frequency.