  Computing the Fr\'{e}chet distance for surfaces is a surprisingly hard
problem and the only known algorithm is limited to computing it between flat
surfaces. We adapt this algorithm to create one for computing the Fr\'{e}chet
distance for a class of non-flat surfaces which we call folded polygons.
Unfortunately, the original algorithm cannot be extended directly. We present
three different methods to adapt it. The first of which is a fixed-parameter
tractable algorithm. The second is a polynomial-time approximation algorithm.
Finally, we present a restricted class of folded polygons for which we can
compute the Fr\'{e}chet distance in polynomial time.
