Analytical solutions are found for the transient starting flow due to a sudden pressure gradient in cylindrical, rectangular, and parallel plate ducts fill with a Darcy- Brinkman porous medium. It is found that, for all geometries, the initial velocity front is flat. It eventually becomes more parabolic for small porous media parameter s but remains flat for large s. The boundary layer thickness is of order (1/s). The transient is also shorter (proportional to exp(-s(2)t)) for large s.