The finite element software of MIDAS is used to establish the arch ring model (M1) and the joint action model (M2) of arch ring - and spandrel structure. The open spandrel hingeless arch bridge is simulated. The joint action coefficient K is introduced to compare and analyze the temperature response of the main arch under two structural states. The analysis results show that the spandrel packing can restrain the deformation of the arch bridge, improve the stress distribution and enhance the stability of the arch ring. Under the temperature condition, the combined effect of the arch ring - the spandrel structure is significant.