In recent years, along with the increase in the size and complexity of computational models, the scenario of mixed-dimensional (e.g., 2D-1D or 3D-2D, and in general HighD-LowD) coupling has drawn a lot of attention. Fields of application where this scenario is of special interest include, among others, (a) blood-flow analysis, (b) hydrological and geophysical flow models, and (c) elastic structures. In this talk the application of mixed-dimensional analysis to time-dependent wave problems governed by the equations of elastodynamics will be discussed. A special challenge is the attack of elastic problems involving out-of-plane bending. The difficulty lies in the fact that there is a mismatch in the type of unknown variables between the HighD and LowD models, and that there is a significant difference between the types of differential equations and possibly also between the types of finite elements (C0 vs. C1) used in each part of the problem [1]. As a particular example, wave propagation will be considered in a 2D elastic structure, which includes a relatively small region whose behavior is fully 2D and a long and slender region whose bending behavior is like that of a Timoshenko beam. To save in computational effort, the latter region is reduced to a genuinely 1D Timoshenko beam [2]. The mathematical and computational problem posed then involves the coupling of the two regions, such that a well-posed, accurate, numerically stable and efficient hybrid 2D-elastic-Timoshenko-beam model is formed. The appropriate interface conditions will be derived, and the well-posedness of the time-dependent problem will be proved. A new computational coupling method is proposed, where the shape functions associated with the axial degrees of freedom on the interface of the elastic solid are modified in a special manner, to allow for the rotation continuity. The method results in a symmetric, positive and stable finite element formulation. Numerical examples will be presented which demonstrate the performance of the scheme.