The ability to predict gas-solids critical flow is a stringent test of the hydrodynamic model of fluidization. It is much more difficult to predict than single-phase compressible critical flow since there are many different two-phase momentum equation formulations in the literature. The hydrodynamic model presented in this paper, and used to analyze critical discharge flow from a non-aerated hopper containing a square obstacle, has already been validated extensively for a wide variety of experiments. The primary objective of this paper is to directly assess the computational ability of this hydrodynamic model to properly predict gas-solids critical flow. To our knowledge, such an assessment has not been previously performed in the open literature. Agreement with the solids velocity data obtained from particle position measurements using motion pictures is excellent. Important qualitatively observed physical phenomena, such as solids buildup on top and oscillating voidage below the square obstacle, are also predicted.