A polarizable electrostatic potential model for classical molecular mechanics is presented. Based on the chemical potential equalization (CPE) principle, the model is developed starting from the original formulation of Mortier, Ghosh, and Shankar [J. Am. Chem. Soc. 108, 4315 (1986)]. Following York and Yang [J. Chem. Phys. 104, 159 (1996)] we present an SP-basis CPE parametrization to describe realistically any sort of molecular system. By fitting ab initio electronic properties, such as dipole moment, polarizability and global molecular hardness of a restricted set of organic molecules, we derive atomic parameters to be applied to a more vast target set of compounds. We show, indeed, that the atomic CPE parameters calculated for the learning set of molecules give reliable values for several electronic properties of various compounds not included in the learning set. The multipole moments obtained by using the proposed CPE parametrization are compared to the results of a fixed charge parametrization like that used by a popular classical molecular mechanics force field, such as AMBER. We show that the fixed charge parametrization can well reproduce only the multipole moments of the molecular conformation or the isomer used for the fit, while being inaccurate when different molecular conformations or isomers are considered. On the contrary, the CPE model realistically reproduces the charge reorganization due to nuclear structural changes of the molecule, such as isomerization or conformational transition. The CPE model has been also tested on various molecular complexes to investigate the polarization response in the case of realistic molecule-molecule interactions. The main result of the paper is the demonstration that the construction of a general polarizable electrostatic force field for classical molecular mechanics is now a viable way.