This paper investigates the hydrodynamics of a bent elastic tube with an instantaneously deformed wall using an arbitrary Lagrangian–Eulerian (ALE) finite element method. The study reveals that the tube deforms continuously with the fluid’s progression, exhibiting diverse deformation patterns. The flow patterns do not adhere to Poiseuille’s profile, with higher velocities detected on the inner side of the bent region during deformation. The results deepen insights into hydrodynamics within bent elastic tubes and bring significance for the design of curved pipelines.