We have performed first-principles calculations to investigate the electronic structure, configurations, formation, and binding energies of native and radiation induced point defects in pristine and Sc-doped wurtzite AlN. For the native defects, the nitrogen vacancy has the lowest formation energy in p-type material while the aluminum vacancy has the lowest formation energy in n-type material which is consistent with the previous studies. Several interstitial defect structures were modeled for Al, N, and Sc atoms. The effects of charge state on their relative stability were investigated. The binding energy of Sc with point defects was calculated and found to be dependent strongly on the defect type and charge state. The results obtained are discussed in light of the possible Sc effects on the radiation damage evolution in AlN. Thus the attraction of Sc atom to N vacancy and both Al and N interstitials reduces their mobility and increases Frenkel pair recombination distance.