Purpose –The main purpose of this paper is to propose a numerical model, which represents the dynamic responses of elastic steel-concrete beams. Design/methodology/approach –The numerical model is based on the lumped system with the combination of the transfer matrix method (TMM) and the analog beam methods (ABM). The beams which are widely used in constructions of highway bridges are composed of an upper concrete slab and a lower steel beam, connected at the interface by shear transmitting studs. The field and point transfer matrices for the beam element of the elastic composite beams are derived. The present model is verified and applied to study the dynamic response of elastic composite beams subject to both moving force and mass. The effects of shear stiffness between the upper slab and lower beam and moving load velocity on the steel-concrete beams deflection are shown. Findings –Results indicate that the maximum deflection in the composite beam subjected to moving load, is significantly affected by the level of interaction between sub-beams and by the load type and velocity. Originality/value – Recently, a numerical model based on the lumped system with the combination of the TMM and the ABM was proposed to study the response of elastic steel-concrete beams with partial interaction, limited to static loading solely. In this study, the current proposed model is developed to study the dynamic response of steel-concrete beams with partial interaction due to moving loads of various velocities. The advantage of the proposed model, unlike previous models that are based on the combination of (TMM) and (ABM), is the ability to study the dynamic behavior of the elastic steel-concrete beams with various end and intermediate conditions and different types and velocities of moving loads. Key Words: Numerical model, Lumped system, Steel-concrete elastic composite beams, Dynamic analysis.