This paper presents a system modeling technique for a high-speed gantry-type machine tool driven by linear motors. One feed axis of the investigated machine tool is driven by the joint thrust from two parallel linear motors. These two parallel motors are coupled mechanically to form the Y-axis while another standalone motor fixed to a support forms the X-axis. The components in the X-axis, which is treated as the mechanical coupling, are carried by the slides of the Y-axis motors. This configuration is applied to improve the dynamic stiffness of the system and operation speed/acceleration. However, the precise synchronous control of the two parallel and coupled motors would be the major challenge. To overcome this challenge, a multivariable system identification method is developed in this paper. This method is used to construct an accurate system mathematical model for the target coupled system. A synchronous control scheme is then applied to the model obtained using the proposed technique. The performance of the system is experimentally verified with a high-speed S-curve motion profile. The results substantiate the constructed system model and demonstrate the effectiveness of the control scheme.