We have modeled the pulsations of HR 1217 (HD 24712), one of the best observed roAp (rapidly oscillating Ap) stars, by taking into account the nonadiabatic effect of radiation as well as the effect of the magnetic field assuming dipole fields. Since the observed frequencies are all above the critical frequencies of our models, a running wave outer boundary condition was imposed. All the oscillation modes examined for the observed frequency range are found to be damped; i.e, the K-mechanism excitation in the hydrogen-ionization zone is not strong enough. We probably need a new mechanism to excite p-modes in the cool roAp star HR 1217. The main pulsation frequency (2.721 mHz) is matched with a quasi-quadrapole mode (l m = 2, where l m is defined as effective latitudinal degree), and the highest frequency (2.806 mHz) obtained in a WET campaign is matched with an l m = 3 mode. Theoretical predictions for the distribution of the pulsation amplitudes and phases with respect to the optical depth agree reasonably with the results of spectroscopic analyses. We also show that the theoretical amplitude modulations with rotation phase agree qualitatively with the observed modulation.