Bridges in seismically active zones have to be designed with special considerations of the dynamic forces caused by an earthquake. These forces acting on the various components of a bridge and their effects on the bridge as a whole structure have to be carefullS’ evaluated to ensure its stability and its availability for rescue operations during an earthquake. An earthquake or an explosion gives rise to unsteady flow at the bridge piers. This kind of flow occurs also when a flood wave or a tidal wave moves past a pier, an intake or a light-house tower. Evaluation of forces on structures in unsteady flow is an important consideration in their design. The problem is mathematically involved and exact solutions are available only for a few elementary shapes of these structures. Histori.- cally, Stokes'” calculated this force on a circular cylinder in 1850. In 1920 Riabouchinsky’o, obtained expressions for these forces on rectangular cylil\ders. In 1933 Westergaard”o, gave a solution to determine the pressures on a rectangular vertical dam subjected to horizontal acceleration. Jacobsen'” in 1949 gave the solution for a cylindrical pier taking into account the free·surface condition. In 1957 Stelson and Mavis'” reported experimental results of the hydrodynamic forces on rectangular piers. In the analysis of these problems the Laplace equation in the appropriate coordinate system is solved for the boundary conditions, namely, that the liquid in contact with a rigid wall sticks to it and that the pressure on the free surface is constant, and the solution implies’ an ideal fluid. Bharat Singh and A.K. Jain'” compared their measurements with Jacobsen’, theory for circular piers and with Westergaard’s theory for rectangular piers. The American and the Indian'” practices are based on Lamb’s cylinder analogy (a misnomer !) ant:! Westergaard’s theory. Riabouchinskey’s theory has been overlooked by the earthquake engineers although his analysis like that of Jacobsen’s is rational and valid for rectangular piers. On the other hand, application of Westergaard’s theory to rectangular piers is questionable. These aspects are examined in this paper. Dimensionless graphs are given to facilitate calculation of the hydro·dynamic forces on circular and rectangular piers.