Discontinuous deformation analysis (DDA) provides a powerful numerical tool for the analysis of discontinuous media. This method has been widely applied to the 2D analysis of discontinuous deformation. However, it is hindered from analyzing 3D rock engineering problems mainly due to the lack of reliable 3D contact detection algorithms for polyhedra.Contact detection is a key in 3-D DDA analysis. The limitations and advantages of existing contact detection schemes are discussed in this paper, and a new approach, called the incision body (IB), is proposed, taking into account the advantages of the existing methods. A computer code 3DIB, which uses the IB scheme as a 3D contact detection algorithm, was programmed with Visual C++. Static and dynamic stability analysis for three realistic engineering problems has been carried out. Furthermore, the focus is on studying the stability of a gravity dam on jointed rock foundation and dynamic stability of a fractured gravity dam subject to earthquake shaking. The simulation results show that the program 3DIB and incision body scheme are capable of detecting 3D block contacts correctly and hence simulating the open-close and slide process of jointed block masses. In addition, the code 3DIB could provide an effective tool for evaluating the safety of 3D dam structures, which is quite important for engineering problems.