Folding structures can be a smart solution for effective transportation, economizing space and for quick assemblage to save time and labor at construction sites. Although some frames with special mechanisms, so-called deployable structures, have been proposed, very few have been done for folding of general frame structures. In this paper a numerical procedure to find one of the optimum paths to fold general frame structures into a desired configuration is proposed. Concepts of the minimum displacement path and the geometrical measurer are introduced in order to assess the validity of computed folding paths. The minimum displacement path gives a compact path in which the movement of frames is minimized to reach the desired configuration. Therefore the obtained results can be applied to not only quick and economical construction but also quick and safe demolishing of frame structures. Further, in the paper, a numerical example indicates the existence of bifurcation points in the folding path. The definition of the bifurcation point on a folding path and how to overcome it are discussed. Two illustrative examples are presented and how to compare the effectiveness of paths among different folding paths is demonstrated. Classification of bifurcation paths at a bifurcation point is successfully attempted with the aid of the group theoretic approach. The infinitesimal number of possible post bifurcation paths can be attributed to the finite number of paths represented by its symmetry.