The single-crystal elastic constants, the Raman and IR frequencies, the isotropic average of the elastic constants, and the first pressure derivatives of these quantities have been calculated for stishovite from a modified rigid ion model. In addition to Coulomb interaction, short-range repulsive interaction between first and second nearest neighbors and angle-bending forces for the oxygen-silicon-oxygen angles are included. The parameters of the model are determined from a least squares fit to the available zero-pressure elastic and optical data in the isostructural sequence SiO2, GeO2, and SnO2. The results for the isotropic bulk modulus and for the shear modulus are K=3.145 Mbar and μ=2.03 Mbar and for their pressure derivatives, (∂K/∂P) =7.0 and (∂μ/∂P) =1.13.