Tlie compressil~le time-dependent Navier-St.okes equations were solved numerically for flows in circular const.ricted ducts. Two types of const.ricted duct geometries wdre employed. a snlootli cosine form constriction and a st,ep like const.rict,ion. Time asgmpt,ot.ic st,eady-stat.e so1ut.ions have been obtained for low Mach number flows. The computations were performed with an implicit approximat,e factorization algorithm. The application of the inflow-outflow boundary conditions was critical for convergence t.o the steady state. The numerical solut,ion correctly predict.ed t.he pressure rise and the resulting flow separation in the expanding part of the duct. The low Mach number solutions for ducts with smooth constri'ct.ion have been compared with experimental dat,a for liquid flows and with results for incompressible flow solutions. Finally, the results for the flow in a duct with a step constriction are given. It is concluded that a low Mac11 number compressible approach may be applied to the studies of unsteady flow phenomena with success.