Mechanical systems including conveyor belts, band saw blades, and power transmission belts are influenced by the lateral motion of the moving structure. This phenomenon was studied in the literature both using the theory of the continuous linear and nonlinear systems and following the multibody technique. The subject is studied by using the finite element method (FEM) validated with reference to the analytical models described in the literature. The contributions of the Coriolis forces, the negative stiffness linked to the transport speed, and the bending stiffness due to the transverse moment of inertia are discussed. The dynamic behavior of a prototypical belt transmission layout with two fixed pulleys and an automatic tensioner is then analyzed. The results show the effect of the transport speed on the reduction of the flexural natural frequencies of the mode shapes strictly related to the lateral motion of the belt span and evidence the design strategy that needs to be followed for a correct operation of the whole system.