Continuous deep beams (CDBs) are the most used members in constructions with highly exposing to different types of dynamic loads. It is well known that; the concrete is a brittle material and has a weak resistance to energy absorption. Using scrapped tire rubber enhances the concrete energy absorption for sustainability purposes. Timoshenko beam theory has been used to solve CDBs subjected to sinusoidal load and has been adopted for verification of numerical results of ANSYS APDL V.15.0. Seven concrete mixes have been simulated with different types and amounts of aggregaterubber replacements. Several parameters have been studied like replacing type, percentages, shear span of beam to depth ratio (a/h) and load intensity. It was found that Timoshenko beam theory can be used for harmonic loading CDBs. Furthermore, replacement in general provided more ductility due to rubber elasticity property. Gravel replacement by 45% has the larger displacement values among the other types. Also, it has been noted that, the sensitive of concrete deep beams towards a/h ratio stills considerable for harmonic loads, i.e. minimizing the ratio leads to decrementing the deflection wave amplitudes.