One of the important applications of the space tethered system is formation flying. To satisfy the requirement for interferometry of ground targets by remote-sensing satellites, a new type of tethered solar sail spacecraft has been proposed in recent research. The replacement of subsatellites of conventional tethered satellite systems with solar sail spacecraft allows for a special formation configuration in which the main satellite is in sun-synchronous orbit and the subsolar sail is in displaced orbit. If the solar sail is at the appropriate attitude, the main satellite and the solar sail spacecraft connected by metal tethers could move side by side, hence this formation system is called transverse formation. The relative baseline of this transverse formation system is perpendicular to the ground trajectory of the satellite, effectively solving the problem that the relative baseline of conventional orbital formations varies in a trigonometric cycle. Researchers on the past ignored the mass and elasticity of the tether, and considered the tether just a constraint in the model system. Since the solar sail is generally quite light compared to the other components of the system, the model inaccuracy caused by ignoring the mass of the tether on the dynamic model and control is extremely obvious. This paper investigates the relative dynamics and control of a proposed system during the deployment process with the mass of the tether. Two precise models of satellite-sail systems are established. One is based on the dumbbell model with the mass tether for the tethered satellite system, and the other is on the basis of the beads model of a tethered satellite system. The rigid one is for control design and the flexible one is for dynamic simulation. It is concluded that the length of the tether and attitude angle of the transverse formation configuration can be decoupled and controlled separately. On the basis of the models, a length rate and LQR control law is developed and the control of the deployment and retrieval process of the tethered solar sail system is investigated. Numerical simulations are performed to verify the accuracy of the conclusions.