Predicting the sound insulation of an engineering system is a complex problem since not only the direct path through a separating element but also the flanking transmission paths can largely influence the sound insulation of the system. When conventionally analyzing flanking transmission, a diffuse field is assumed in the walls and floors, which are modelled as plates. The junction connecting the walls and floors is assumed to be of infinite extent and the transmission of vibration across the junction is calculated by integrating over all possible angles of incidence. Due to the limitations of the conventional approach, a new approach based on diffuse field reciprocity is proposed. The diffuse field reciprocity relationship relates the vibration transmission to the direct field of a diffuse subsystem to the direct field dynamic stiffness of the subsystem, i.e., the dynamic stiffness of the equivalent infinite subsystem as observed at the junction. The direct field dynamic stiffness matrices of thin, isotropic, elastic plates can be analytically derived. For more complex walls or floors a possible approach is to calculate the direct field dynamic stiffness using finite elements and perfectly matched layers. The perfectly matched layer surrounding the finite element model absorbs the wave propagating outwards from the bounded domain, thus simulating an infinite subsystem.