Summary: This paper presents a method of analysis of undamped vibrations of continuous beams with rigid and/or elastic supports induced by moving distributed loads. Inertial effects of moving loads are also taken into account. As opposed to some of the well established methods of dynamic analysis of continuous beams (e.g. the slope-deflection method, the method of initial parameters, etc.) the present method is reduced to the solution of integral equations of Volterra type to obtain dynamic reactions of internal supports. With calculated reaction forces dynamic deflection and other quantities of interest are given by infinite series.