Oscillatory (or pulsatile) flow in ducts filled with a Darcy-Brinkman medium is studied. Analytic solutions (some in closed form) are derived for the annular duct, the rectangular duct and the sector duct. These exact solutions also serve as accuracy standards for approximate and numerical solutions. The problem is governed by two parameters, a non-dimensional frequency and a porous medium factor, which is inversely proportional to the Darcy number. The effects of these parameters on the amplitude and phase lag of the flow are discussed.