We present an original treatment for the finite bending of curved pipes with arbitrary cross sections. The curved pipe is successively regarded as a three-dimensional continuum and a shell, and a formulation is proposed for each model. We show that, from a numerical point of view, the finite bending problem is reducible to an axisymmetric analysis augmented with 1 d.f. We also show how to take advantage of this analogy to solve the bending problem using standard axisymmetric FE routines