Understanding the channel depth around bridge piers, whose side face is inclined as a consequence of local scour, requires the analysis of the interaction between flow and structure through the physical and numerical simulation and field measurements. Over the years, tests have been performed through physical simulation and field measurements; however, this paper contributes through the numerical simulation to the study of the effect produced by the inclination of the pier face on the phenomenon of local scour. The three-dimensional software ANSYS CFX was used which has the capacity to simulate the flow dynamics through the bridge pier. Thus, water flow patterns such as direction and velocity have been analyzed to find the relationship that they have with the local scour. The study was made with two shapes of piers; the first one reduces the transversal section from the top to the smaller bottom base, and the second shape reduces the transversal section from the bottom to the smaller top base. The results show that the first type of shape was favorable to generate greater scour depth, finding velocities greater than 50% in the pier face.