This paper presents folded surface detection and tracking for augmented maps. For the detection, plane detection is iteratively applied to 2D correspondences between an input image and a reference plane because the folded surface is composed of multiple planes. In order to compute the exact folding line from the detected planes, the intersection line of the planes is computed from their positional relationship. After the detection is done, each plane is individually tracked by frame-by-frame descriptor update. For a natural augmentation on the folded surface, we overlay virtual geographic data on each detected plane. The user can interact with the geographic data by finger pointing because the finger tip of the user is also detected during the tracking. As scenario of use, some interactions on the folded surface are introduced. Experimental results show the accuracy and performance of folded surface detection for evaluating the effectiveness of our approach.