Disclosed is a fairing element intended to be placed in a passage for flow of a fluid, in order to surround an obstacle which crosses the passage so that the fairing element guides the flow of the fluid on two opposite sides of the obstacle. The fairing element is designed such that the pressure of the flowing fluid is constant or approximately constant in an upstream part of the suction surface of the fairing element. A fairing element of this kind can be incorporated into a stator of a turbomachine, in particular of an aircraft turbomachine.