Summary: Aiming to unfold the flanged and locally bulged part on finite element mesh surface, a Geometry Unfolding (GU) algorithm is proposed in order to unfold the special part. This new algorithm improves the old flange geometry unfolding algorithm [1] and can automatically adapt the flanged and locally bulged part on both plane and surface. The 3-D graphics geometry transform method is used to unfold the flanged region, and then the implicit surface based on radical basis function is used to unfold the locally bulged region. GU algorithm can also deal with mixed meshes of elements, such as triangle and quadrangle elements. The program of the GU algorithm independently developed can identify the unfolding elements automatically, and unfold on finite mesh surface rapidly and effectively.