When a thin sheet of a flexible material such as paper is fed from a horizontal spool towards
a rough horizontal plane below it, the sheet folds on itself in a regular manner. We model
this phenomenon as a free boundary problem for a nonlinearly elastic sheet, taking into
account the stiffness and weight of the sheet and the height of the spool above the plane.
By using a continuation scheme we solve the problem numerically and follow the evolution
of one period of the fold for various values of the parameters. The results are found to
agree well with observations of the folding of paper sheets.