The dynamic stability of the lateral response of a simply supported Bernoulli-Euler beam carrying a continuous series of equally spaced mass particles is analyzed. The beam rests on a uniform elastic foundation and damping is considered by including a distributed viscous damping coefficient. The particles are restricted to constant speed. The Galerkin method is used to generate a set of approximate governing equations of motion possessing periodic coefficients. Floquet theory is utilized to study the parametric regions of stability which are displayed in graphical form.