Solutions to the problem of cable-stayed bridge dynamics are received and analysed on the basis of two modelling options. According to the first one space-time finite-elements are used. The first three bridge vibration modes are shown to study cable-stayed bridge fluctuations when exposed to the vertical force moving at a constant speed and compile charts of time history strains in fixed sections of a deck. According to the second option a suspended superstructure is represented by a fold with absolutely rigid transverse membranes in joints of cables, a bridge tower is represented by a beam. Natural modes of the bridge are received by a solution of homogeneous system equations of the mixed method. Nodal lines of a fold for the first four natural modes are shown. The comparative description of applicability of the above-mentioned methods of solving problems of dynamics affected by moving load is given.