A no-insulation (NI) REBCO superconducting magnet is under development at Wuhan National High Magnetic Field Center, China. The magnet with the liquid helium cryostat system has a compact structure to reduce the space required for operation. During a quench, the fast-changing spatial magnetic field around the NI magnet may induce a strong eddy current in the conductive parts of the cryostat. The eddy current and its associated Lorentz force will generate mechanical stress on the cryostat, especially on the thermal shield (TS). The mechanical strength of the cryostat needs verification in the preliminary design. Furthermore, the degree to which the electromagnetic coupling between the cryostat and NI magnet might impact the quench behaviors of the NI magnet remains uncertain. In this paper, a multi-physics quench model is newly developed for the NI REBCO magnet, and the alternating direction implicit method is employed for the solver of the thermal model to improve computational efficiency. This simulation model can consider the electromagnetic coupling effect between the NI magnet and cryostat by constructing a partial element equivalent circuit. A quench analysis has been performed and we found that: (1) The cryostat can function as a secondary shorted circuit to the NI magnet and slow down the quench speed to a certain extent. (2) During the rather fast inductive quench phase, the cryostat will experience an attraction force towards the quench propagation frontier. (3) A quench propagation from one end of the magnet can cause a significant z-axis unbalanced force on the TS. (4) Cryostat materials with drastically changed electrical conductivity can significantly affect their mechanical responses during a quench. However, the eddy current density and maximum Von Mises stress on the TS are barely affected by the thickness of the TS and the contact resistance of the NI REBCO magnet.