A thin flexible inextensible rope fed continuously from a fixed height and falling on a horizontal plane usually forms a circular coil. This phenomenon is analysed as a geometrically nonlinear free-boundary problem for a linearly elastic rope. The stiffness and velocity of the rope, the height from which it is fed and gravity are taken into account. The problem is solved by using a numerical continuation scheme. The coil radius is determined as a function of the various parameters. Tables and graphs of the results are presented.