This paper deals with a problem of numerical solution of laminar viscous incompressible stationary and nonstationary flows through a vessel with bypass. One could describe these problems by using model of the Navier-Stokes equations and find a steady solution of an unsteady system by using a multistage
Runge-Kutta method together with a time dependent artificial compressibility method. Nonstationary solution is achieved from initial stationary solution by prescribing of nonstationary outlet conditions. Some results of numerical solution of cardiovascular problems are presented: stationary and nonstationary
2D flows in a vessel and a bypass.