Today, various techniques are utilized in order to eliminate vibrations, shocks and reduce their detrimental effects on the performance of sensitive equipment and industrial machinery. One of the most common and effective methods to isolate the system from troublesome vibrations is using a variety of passive vibration dampers. Among these isolators, the wire rope isolators are well known and high usage devices. In this thesis, in order to reduce vibrations and for vibrational energy absorption of photographic cameras mounted on aircraft and helicopters, the vibrational and hysteresis behavior of a compact wire rope isolator is studied. In this regard, with doing quasi-static and dynamic tests, the hysteresis curves of wire rope isolator in the vertical and horizontal directions have been obtained. Then, using the experimental data in an optimization process, the modified Bouc-Wen model has been identified for description of the wire rope hysteresis curves. Also, the effects of speed and vertical preload on the hysteresis behavior of the wire rope isolator have been shown. Next, to evaluate the effects of frequency and amplitude on hysteresis curves of wire rope isolator, vertical and horizontal dynamic tests with different excitation amplitudes and frequencies (in range of 16 to 120 Hz) have carried out. These tests indicate that the hysteresis curves of the wire rope isolator are both amplitude-dependent and frequency-dependent and the frequency dependence is demolished at higher frequencies far from the resonant frequency. Given the diversity in the shape of hysteresis curves at different frequencies and amplitudes, an artificial neural network (ANN) model has been proposed to model the dynamic and quasi-static hysteresis behavior of the wire rope isolator simultaneously. Based on the NN model, a parametric analysis for vertical and horizontal loading is performed and the results are presented. In another part of the thesis, the precise geometric model of the wire rope isolator has been created in CATIA software and has been used for finite element simulating of the quasi-static behavior of the wire rope isolator. The simulation has been performed in ABAQUS finite element software. Comparing the results of the mathematical modified Bouc-Wen model with experimental results and also, comparing the results of identified NN model with experimental results for test data confirms the high accuracy of these models in prediction the hysteresis behavior of the wire rope isolator. Keywords: Wire rope isolator, Hysteresis curve, Modified Bouc-Wen model, Artificial neural network (ANN) model, Finite element simulation