A new generalized analytical theoretical model of thermal conductivity for multilayer nanostructures based on nitride semiconductors is proposed. The developed theory qualitatively complements and generalizes the investigations, the results of which were performed for one- or two-layer nanostructures. The theory has its mathematical basis for the application of another type of boundary conditions for the components of the phonon field and components of the stress tensor. The obtained results can be performed to describe the processes associated with the theoretical conductivity of nanostructures with an arbitrary number of layers in them. The proposed theoretical investigations are applied to the calculation of the thermal conductivity of experimentally created nanostructures.