A side contact model of joint is proposed, which considers the horizontal distance distribution and side contact between the asperities on the contact surfaces. The Leica DCM3D microscope is applied to collect the profile data of the grinding surfaces. After analyzing the profile data by the statistical method, it is found that the horizontal distance distributions between asperities on the contact surfaces show an approximate normal distribution. Based on the discovery, a contact model of joint considering the horizontal distance distribution and side contact between asperities is established by statistical theory. The simulation results of the model show that the dimensionless tangential contact stiffness of joint is always lower than that of the GZQ model under the condition of the same dimensionless average distance of contact surfaces and P/T. When the standard deviation of horizontal distance between asperities decreases, both the dimensionless tangential contact stiffness of joint and the dimensionless normal contact stiffness increase. The finite element analysis and the modal experiment based on the contact model are carried out. It is found that the first three modal frequencies and modal shapes obtained from finite element analysis are in good agreement with those from the modal experiment, and compared with the modal frequencies from experiment, the modal frequencies from finite element analysis based on the model proposed in this paper show less error than those of finite element analysis based on the GZQ model. Therefore, this model proposed in this paper can more accurately predict the dynamic characteristics of joint.