A shell model potential for silica and protonated zeolite catalysts is presented. The potential parameters are fitted exclusively to ab initio data generated by nonempirical quantum chemical calculations on small molecular models made of SiO4 and AlO4 tetrahedra. The Hartree-Fock method has been used with a basis set of double zeta + polarization quality on Si, Al, and H atoms and of valence triple zeta + polarization quality on O atoms. Comparison is made with an ab initio molecular mechanics force field previously derived from the same data and with an empirical parametrization of the shell model potential. The power of the new potential for predicting the crystal structures and the properties is demonstrated for a variety of silica and zeolite structure types. Cell parameters of dense and microporous silica are predicted with a mean error of 1.8%. Compared to earlier potentials, substantial progress is made in predicting dynamical properties. Examples are the phonon dispersion curves of alpha-quartz and the infrared spectrum of zeolite ZSM-5. As a first application to acidic zeolite catalysts the local structures and vibrational frequencies of the different bridging hydroxyl groups in faujasite are calculated. The results do not show the artifacts exhibited by previous potentials.