Structural correlations at the Si(111)/Si3N4(0001) interface are studied using the molecular dynamics (MD) method. In the bulk, Si is described by the Stillinger-Weber potential and Si3N4 by an interaction potential which contains two-body (steric, Coulomb, electronic polarizabilities) and three-body (bond bending and stretching) terms. At the interface, the charge transfer from silicon to nitrogen is taken from LCAO electronic structure calculations. Using these Si, Si3N4 and interface interactions in MD simulations, the interface structure (atomic positions, bond lengths, and bond angles) is determined. Results for fracture in silicon are also presented.