Validity of a force field with explicit treatment of electrostatic polarization in a form of inducible point dipoles for computing acidity constants was tested by calculating absolute pK(a) values of substituted phenols, methanol, and imidazole in water with the molecular dynamics technique. The last two systems were selected as tyrosine and histidine side-chain analogues, respectively. The solvent was represented by an explicit polarizable water model. Similar calculations were also performed with a modified OPLS-AA nonpolarizable force field. The resulting pKa values were compared with available experimental data. While the nonpolarizable force field yields errors of about 5 units in the absolute pKa values for the phenols and methanol, the polarizable force field produces the acidity constant values within a ca. 0.8 units accuracy. For the case of imidazole, the fixed-charges force field was capable of reproducing the experimental value of pK(a) (6.4 versus the experimental 7.0 units), but only at a cost of dramatically underestimating dimerization energy for the imidazolium -water complex. At the same time, the polarizable force field yields an even more accurate result of pK(a) = 6.96 without any sacrifice of the accuracy in the dimerization energy. It has also been demonstrated that application of Ewald summation for the long-range electrostatics is important, and substitution of a simple cutoff procedure with Born correction for ions can lead to underestimation of absolute pKa values by more than 5 units. The accuracy of the absolute acidity constants computed with the polarizable force field is very encouraging and opens road for further tests on more diverse organic molecules sets, as well as on proteins.