We have examined the radiative corrections to $\ensuremath{\mu}$ decay in the SO(3) gauge model. Quantizing a theory in the generalized ${R}_{\ensuremath{\eta}}$ formalism, we have proved by actual calculation that the theory yields a gauge-independent $S$ matrix and is unitary when all the contributions are summed up. Taking the dimensional regularization method, we carried out the renormalization program in the Landau gauge, in which the ultraviolet divergences are shown to be eliminated by rescaling of the independent physical parameters and the wave functions in the original gauge-symmetric Lagrangian. We have also shown how to introduce an infinitesimally small mass to a photon without breaking the renormalizability of the theory in order to treat the infrared problem. We have then obtained the finite radiative corrections to $\ensuremath{\mu}$ decay without either ultraviolet or infrared divergences. The theory is indistinguishable from the classical theories of weak interactions as long as we observe only the $\ensuremath{\mu}$ decay, neglecting terms of order $O(\frac{\ensuremath{\alpha}m_{f}^{}{}_{}{}^{2}}{M_{W}^{}{}_{}{}^{2}})$. Similarly, we have computed the finite radiative corrections to $\ensuremath{\beta}$ decay. The ratio of $\ensuremath{\mu}$- and $\ensuremath{\beta}$-decay coupling constants is now model-dependent. In the case of the SO(3) gauge model, it depends on the fermion mass spectra of the model.