Investigated in this paper is the first on the moving-load-caused nonlinear coupled dynamics of beam-mass systems. A constant value load excites the beam-mass system where its position on the beam-mass system changes periodically. The energy contribution of the moving load is included via a virtual work formulation. The kinetic energy of the mass together with the beam as well as energy stored in the beam after deflection is formulated. Hamilton’s principle gives nonlinear equations of the beam-mass system under a moving load in a coupled transverse/longitudinal form. A weighted-residual-based discretisation gives a 20 degree of freedom which is numerically integrated via continuation/time integration along with Floquet theory techniques. The resonance dynamics in time, frequency, and spatial domains is investigated. As we shall see, torus bifurcations are present for some beam-mass structure parameters as well as travelling waves. A finite element analysis is performed for a simpler linear version of the problem for to-some-extend verifications.