In this paper a theoretical and experimental analysis is proposed for elastic wave propagation in heterogeneous waveguides of a rectangular cross section. A formulation is presented which is based on approximate fields of displacement and stress which satisfy exactly the continuity conditions at interfaces and boundary conditions on lateral faces. Two types of waveguides are envisaged: a so‐called rectangular clad‐core guide and a guide made of three superimposed layers, the materials involved being orthotropic. The linear elastodynamics of these guides is deduced from a two‐field variational formulation of the Hellinger–Reissner type. Dispersion spectra are constructed for both types of waveguides depending on the concentration and relative arrangement of the different materials which build up the guides. Geometrical and material conditions deduced from the values of asymptotic speeds are proposed in order to guarantee the propagation of a certain mode in a prescribed region of the guide. Dispersion gauges are introduced with a view to controlling the dispersion which strongly depends on the nature and arrangement of materials. Experimental results obtained by a resonance method are reported for the two types of rectangular guides. The dispersion observed and the existence of guided modes are reported. Finally, comparison is made between theoretical predictions and experimental results, which proves that the predictions were correct.