1. A vibration testing system for repetitively performing a series of processes including numerical simulation, waveform generation, actuator driving, and measurement, comprising: one or a plurality of shaking systems each having an actuator with a movable part for applying deformation to a specimen, a control sensor for measuring a driving state of the shaking machine, an actuator controller for controlling the driving state of the actuator by using an input command signal and an output of the control sensor, and a monitor sensor for measuring a response state of the specimen; and a computer system in which one or a plurality of computers provide a measurement processing function of processing an output of the monitor sensor in a format capable of being used by a numerical simulation function, the numerical simulation function of calculating a vibration response at a predetermined time interval in accordance with a preset structure numerical model, a process result of the measurement processing function, and a time function given as an external force applied to a structure, and a waveform generating function of calculating the time function of deformation to be applied to the specimen in accordance with a process result of the numerical simulation function and outputting the calculated time function to the shaking machine controller, wherein said computer system provides: a model substituting function of modeling characteristics of the specimen to be shaken by the shaking system by using the finite number of parameters, calculating a specimen response quantity with respect to actuator driving state, and inputting the response quantity to the numerical simulation function; a parameter modification function of comparing a calculation result of the model substituting function and a process result of the measurement processing function and modifying the values of the parameters so that characteristics of a specimen formed by the model substituting function are made generally coincident with the characteristics of the actual specimen; and an abnormality inspection function of judging an operation state of each shaking system and substituting the process result of the measurement processing function to be passed to the numerical simulation function to a process result of the model substituting function when an abnormal operating state is defected.