Using an isothermal axisymmetric MHD model of the solar corona with transparent boundary conditions, we study how coronal loops with apex height between one third and two solar radii react to Alfvén waves generated at the base of the corona. The first response is a steady increase of the density along the excited loops. Density oscillations are also observed, along the apex of the longest loops, that is, those along which waves are substantially damped. Both the steady and the oscillating component scale as the square of the Alfvén wave amplitude, and accordingly, the frequency is double that of the mother wave. Siphon flows may also appear, along short or long loops, depending on whether both or a single foot-point of the loop system is excited.