In this paper, the shock waves propagating in a rectangular elbow were investigated numerically in order to clarify how the transmitted shock wave past the elbow is stabilized to the uniform shock and the flow field induced by the shock. The computations were carried out by solving the two-dimensional compressible Navier-Stokes equations by means of the TVD finite difference method. The calculations were performed for three incident shock strengths and three Reynolds numbers of the flow, and the flow fields were expressed by contour lines of pressure, density and the vorticity, velocity vectors, stream lines, pressure distributions and wave diagrams. The numerical results showed that the nonuniformity of the transmitted shock continued for a long distance and the attenuation of the transmitted shock was very slight, and the production of the vortex and the secondary shock wave and their development were observed clearly.