Abstract: Understanding the coupled multiphase flow and solid deformation processes in porous media is a significant issue in the area of developing and utilizing underground resources. This study first established the coupled modeling of compressible two-phase flow and deformation of porous media, which considers capillarity and gravity. Meanwhile, the strong form and the corresponding weak form of coupled multiphase flow and solid deformation model were presented. Then, the capacity of the proposed DG method for the coupled hydromechanical model was verified by comparison with analytical and numerical results of the one-dimensional Terzaghi consolidation problem. Subsequently, the two- and three-dimensional cases were performed to study the flow behaviors and deformation characteristics, respectively. In addition, the effects of the penalty factors \delta _\rms and \delta _\rmf on the stability of the numerical results were analyzed. The simulation results show that gas saturation and pore pressure continually increase with the injection of gas. The increment of pore pressure reduces the effective stress, which results in deformation and expansion of the porous medium. The gas floats up and gathers at the top boundary due to gravity. The decrease of the penalty factors \delta _\rms and \delta _\rmf trends to cause the fluctuation of saturation, pressure, effective stress, and displacement. The increases in penalty factors are beneficial to suppress the discontinuity of the finite element function crossing the elements.