There are many ways to flatten polyhedra continuously. This paper focuses on the maximum number of rigid edges in continuous flattening motions for a given polyhedron. First, we provide an upper bound of the number for each convex polyhedron based on the results described in the literature. Next, for some triangular prisms, we provide two flattening methods that keep more edges rigid. Moreover, using the two flattening methods, we provide continuous flattening motions for some convex quadrangular prisms with 11 edges rigid, i.e., all edges are rigid except for one. As a result, our method achieves the maximum number (precisely 11) of rigid edges in the continuous flattening of the convex quadrangular prisms.