This paper presents an activity concerning the modelling and control of a system adopted to perform shear tests on seismic isolators. The test rig consists of a hydraulic actuation system that drives a sliding table mounted on linear bearings. The system is characterized by non-linearities such as hydraulic proportional valve dead zone and frictions. A non-linear model is derived and then employed for parameter identification procedure. The test rig needs a suitable controller able to guarantee the desired table displacement in presence of unknown reaction force of the device under test. The proposed approach consists of a feedforward control integrated with a feedback one. The feedforward control law takes the form of a non-linear inverse model of the system. In this way, it is possible to obtain the desired target without affecting the stability of the test rig. The feedback control has the function to compensate for tracking error due to the model uncertainties and the unknown isolator reaction force. Therefore, the feedback control is not required to compensate for the large non-linearities: in this manner, it is possible to obtain good tracking results without the increasing of the feedback control gain that would change the stability properties of the plant. Numerical simulations have been performed in order to evaluate the goodness of the designed control with and without the specimen under test. Experimental tests show that the controlled system simulations are able to predict the controller performance. The experimental results also confirm that the performance of the proposed controller fully satisfy the standards concerning the testing procedure of seismic isolators.