Phonon transmission across epitaxial interfaces is studied within the lattice dynamicapproach. The transmission shows weak dependence on frequency for a lattice wave with afixed angle of incidence. The dependence on azimuth angle is found to be related to thesymmetry of the boundary interface. The transmission varies smoothly with the change ofthe incident angle. A critical angle of incidence exists when the phonon is incident from theside with large group velocities to the side with low ones. No significant mode conversion isobserved among different acoustic wave branches at the interface, except when the incidentangle is near the critical value. Our theoretical result of the Kapitza conductanceGK across the Si–Ge(100) interface at temperatureT = 200 Kis 4.6 × 108 W K−1 m−2. A scaling law at low temperature is also reported. Based on the features of transmission obtained withinthe lattice dynamic approach, we propose a simplified formula for thermal conductanceacross the epitaxial interface. A reasonable consistency is found between the calculatedvalues and the experimentally measured ones.