The dynamic responses of the beam under the function of the moving loads are very important practical problem in the strength and stiffness designs and the strength and stiffness checks. The measuring technology of the sensors is no doubt one of the ripe methods in the detections of the structural stresses,The reasonable designs of the electrical measuring sensors are often based on the theoretical analyses,but the theoretical solution of this kinds of problems are often hard to be given. In this paper,the definite mathematical model was proposed before hand; and the model can be divided into two sub-problems considering of the linearity of the problem,then the method of separation of variables and the inherent function method were used to give the theoretical solutions respectively,an numerical example were introduced to give the deflection responses and the stress responses of the simply-supported beam and the dynamic responses of the capacitor of the sensor in order to illustrate the important effects of the dynamic effects. This method can be extended to study the dynamic responses of the beam with an elastic system moving on it.,the given theoretical conclusions have some references to the designs of new electrical sensors.