A quasi-one-dimensional compressible-flow theory in the presence of blowing/suction is presented for shock managementinsidesupersonicinletsandsupersoniccompressorcascades.Thetheorycanpredicttheamountof flow blowing/suctionrequiredtoplacetheshockataprescribedarearatioinadiverging flowpassageastheexitpressure is varied. The formulation is based on classical one-dimensional compressible-flow theories for normal shock waves and flow blowing/suction. Application of the theory to a supersonic nozzle shows that if the exit pressure is higher than the base value, then suction behind the shock or blowing in front of the shock is required to hold the shock stationary. On the other hand, if the exit pressure is lower than the base value, then blowing behind the shock or suction in front of the shock is required. For the case of blowing, the amount required to fix the shock location is a strongfunctionofthestagnationconditionsandtheangleoftheblowing flow.Theresultingtheoryischeckedagainst numerical solutions of the quasi-one-dimensional Euler equations, with excellent agreement between theory and numerical solutions. Applications of the theory to two-dimensional inviscid and two-dimensional viscous flows are