This paper presents an experiment testing the accelerations of a system composed of a magnetorheological elastomer (MRE) and a cuprous mass under displacement excitation. The goal of this paper is to explain the experiment and to present the experimental results (the hysteresis loops). The method of extracting field-dependent material properties of the MRE from the results and further analysis will be presented in a subsequent paper. The experimental results reveal that the mechanical behavior is nonlinear and the field-dependent behavior of the MRE is associated with the applied frequency. (The frequency domain is divided into three ranges according to the field-dependent characteristics of the MRE.) In the low frequency range, the mechanical properties of the MRE change slightly with the applied magnetic field; in the moderate frequency range, the field-dependent properties appear and they are highly nonlinear; in the high frequency range, the field-dependent properties deviate from those of the moderate frequency range, which causes the circled area of the hysteresis loops in the two measured acceleration domains to decrease with the applied magnetic field. To explain the characteristics in the low frequency range, ABAQUS code is used to calculate the zero-field property of the MRE and a point-dipole model is employed to model the field-dependent property approximately.