The Alfve´n modes in inhomogeneous cylindrical current‐carrying plasmas is studied solving numerically the Hain‐Lu¨st equation. We have obtained the eigenfrequencies for different current density and it is shown that the distance of the frequencies from the lower edge of the Alfve´n continuum depends on its profile. We have shown, using the WKB approximation, that there exist a MHD discrete Alafe´n mode. The numerical results of the discrete Alfve´n frequencies are compared with the one obtained using the WKB approach. This study is suitable to understand oscillations and heating in solar prominences and also chromospheric‐coronal heating and oscillations by Alfve´n waves.