In the analysis of the power transmission through junctions between thick plate structures, it is necessary to consider not only the transverse bending motion of the plates but also the in‐plane wave motion. That is, for these types of structures both the shear and rotary inertia effects and the in‐plane wave effects must be considered simultaneously in order to obtain a complete solution to the problem. In this paper, a statistical energy analysis approach is developed to evaluate the power transmission through the junction between two plates in an L‐shaped configuration, where the solution includes the shear and rotary inertia effects (Mindlin bending) and the in‐plane waves effects. Analytical results are presented for the absorption (or transmissibility) of the junction and the ratio between the incident bending wave power and the transmitted waves (bending and in‐plane) power. Results for pure (classical) bending are also presented for comparison with the Mindlin bending results.