Strand structures such as the tails or feelers are common to man-made or natural shapes. The knowledge of strand structures which a shape possesses can be exploited in its matching, recognition, retrieval etc. Although a variety of methods in shape decomposition have been presented, there is still a need for a robust and versatile method to detect the strand structures, especially when the shapes have large deformation or noise. Based on the visibility of points, we design a shape descriptor and propose an effective method to detect the strand structures possessing in 2D shapes. An intuitive idea is that the points in strand structures can only see small number of points from their reference points inside the shape. Meanwhile, the visibility of a point is more robust than its convex-concave features. Extensive experiments have been done on shapes with various kinds of deformation and large noise, demonstrating the robustness and effectiveness of our strand structures detection method.