On multigrid acceleration of flow computations D. Drikakis, O. Iliev, and D. Vassileva Multigrid algorithm for accelerating 2D and 3D incompressible flows computations is presented. The artificial compressibility formulation of the Navier Stokes equations is exploited. The developed multigrid algorithm is of Jameson's type. The smoothing procedure is based on a single grid solver developed earlier by the first author. The influence of different components of the multigrid algorithm on its convergence behaviour is numerically studied and discussed. Special attention is paid on combining two advanced approaches for accelerating computations: multigrid approach and local solution approach. Results from computations of different incompressible flows are presented and discussed.