In this paper, mechanical responses and electro-thermal characteristics of a rare earth barium copper oxide (REBCO) high-temperature superconducting (HTS) insulated pancake coil during the quenching process are investigated through finite element modeling (FEM). Firstly, a two-dimensional axisymmetric electro–magneto–thermal–mechanical FEM model with real dimensions is developed. Based on the FEM model, a systematic study on the effects of the time taken to trigger the system dump, background magnetic field, material properties of constituent layers, and coil size on quench behaviors of an HTS-insulated pancake coil is implemented. The variations in the temperature, current, and stress–strain in the REBCO pancake coil are studied. The results indicate that an increase in the time taken to trigger the system dump can increase the peak temperature of the hot spot but has no influence on the dissipation velocity. An apparent slope change of the radial strain rate is observed when the quench occurs regardless of the background field. During quench protection, the radial stress and strain reach their maximum values and then decrease as the temperature decreases. The axial background magnetic field has a significant influence on the radial stress. Measures to reduce peak stress and strain are also discussed, which indicates that increasing the thermal conductivity of the insulation layer, copper thickness, and inner coil radius can effectively reduce the radial stress and strain.