The modeling and simulation of flexible multibody systems containing fluid-conveying pipes are considered. It is assumed that the mass-flow rate is prescribed and constant and the pipe cross section is piecewise uniform. An existing beam element capable of handling large motions is modified to include the effect of the fluid flow and the initial curvature of the pipe. The modified element is incorporated in a finite-element based multibody system dynamics program, which takes care of the connection with other parts of the system and the simulation. The element is applied in several test problems: the buckling of a simply supported pipe, the flutter instability of a cantilever pipe, and the motion of a curved pipe that can rotate about an axis perpendicular to its plane. As a three-dimensional example, a Coriolis mass-flow rate meter with a U-shaped pipe is considered.