The study of the influence of the bridge piers is still active research topic of interest. The effect of Reynolds number (Re) on the drag coefficients (CD) due to water flow around piers is simulated numerically by solving Navier-Stokes equations. The piers are modelled with different shapes of pier cross section. The comparative studies among the drag coefficients of circular, rectangular, square, octagonal, elliptic and lenticular shaped bridge piers are carried out. A numerical algorithm is presented to explore the influence of variation of velocity on the hydrodynamic force and pressure distribution exerted on piers. The hydrodynamic interactions between wall and fluid medium are presented herein with the help of velocity and pressure contour plots. A significant finding is that the shape of the pier cross section has a significant effect on the fluid pressure exerted on bridge piers. This helps understand the appropriate shape of the bridge piers to be interested in the real applications.