An incompressible unsteady viscous two-dimensional Navier-Stokes solver is developed by using “Consistent Flux Reconstruction” method. In this solver, the full Navier-Stokes equations have been solved numerically using a collocated finite volume scheme. In the present investigation, numerical simulations have been carried out for unconfined flow past a single circular cylinder with both structured and unstructured grids. In structured grid, quadrilateral cells are used whereas triangular elements are used in unstructured grid. Simulations are performed at Reynolds number (Re) = 100 and 200. Flow simulation over a NACA0002 airfoil at Re = 1000 using unstructured grid based solver is also reported. The vortex shedding phenomena is mainly investigated in the flow. It is observed that the nature of flow depends strongly on the value of the Reynolds number. The present results are found to be in satisfactory agreement with several numerical results and a few experimental results available from literature.