In the wind tunnel arrangement under consideration, the air leaves the Laval nozzle as a free jet and is recaptured by the diffuser, which is of the convergent-divergent design. A theoretical analysis of the flow process through this type of supersonic wind tunnel is presented and the diffuser efficiency is calculated for the case of equilibrium between test chamber pressure and pressure in the nozzle exit, assuming one-dimensional, in viscous, steady flow. Using the basic equations of continuity, energy and momentum flux through a bounding surface, an exact solution of the problem is obtained, which is applicable up to Mach number infinite. One of the basic results is, that in the recapturing zone of the diffuser a transition occurs from supersonic to subsonic flow, which is followed by an acceleration in the convergent portion up to sonic velocity at the second throat. The transition is not a normal shock and involves a total pressure loss greater than that of a normal shock at the test section Mach number. A mathematical solution with supersonic velocity after the transition process has no physical existence. A comprehensive comparison of the analytical results with available experiments in supersonic wind tunnels up to Mach number 4.4 regarding diffuser efficiency and second throat area shows good agreement.