The swelling dynamics of long cylindrical gel is analyzed by the stress diffusion coupling model [T. Yamaue and M. Doi, Phys. Rev. E 69, 41402 (2004)]. Two situations are analyzed: (i) stress induced swelling, where the swelling is caused by an elongational force applied on the gel, and (ii) free swelling, where the swelling is caused by thermodynamic force. The relaxation times characterizing these processes are calculated. It is shown that earlier calculations for the relaxation time, which are based on some physical or mathematical approximations, give results surprisingly close to the rigorous calculation, but the difference can be still seen experimentally.