A theoretical solution for a two-dimensional steady flow of a gas-solid mixture exiting a fluidized bed into a vertical standpipe is presented. Initially, analytical expressions for the particle velocity and gas pressure are obtained inside the fluidized bed and standpipe, assuming that changes in the mixture density are negligible. For inertial dominated flow regimes it is shown that the gas pressure at the standpipe entry region is very sensitive to the magnitude of inertial and gravitational forces, which could explain the observed particle and gas flow instabilities in industrial fluidized bed/standpipe systems. When density changes in the gas-solid mixture are considered, it is shown that the granular 'fluid' density varies considerably in the standpipe entry region with the solid fraction increasing near the top edge of the standpipe walls. The rapid density gradients at the standpipe envy are compensated by gas pressure gradients of similar order, yielding gas velocities comparable in magnitude with solid particle velocities. This first approximation solution suggests that the flow of a granular fluid from a fluidized bed into a standpipe may be governed primarily by the particle phase flow behavior, and rapid changes in particle velocity and density at the standpipe entry could potentially propagate downwards into the standpipe, rendering the flow of the granular fluid erratic and difficult to control.