The sensitivity of energetic materials along different crystal directions is not the same and is anisotropic. In order to explore the difference in friction sensitivity of different surfaces, we calculated the structure, excess energy, surface energy, electronic structure, and the nitro group along (1 1 1), (1 1 0), (1 0 1), (0 1 1), (0 0 1), (0 1 0), and (1 0 0) surfaces of EDNA based on density functional theory. The analysis results showed that relative to other surfaces, the (0 0 1) surface has the shortest N-N average bond length, largest N-N average bond population, smallest excess energy and surface energy, widest band gap, and the largest nitro group charge value, which indicates that the (0 0 1) surface has the lowest friction sensitivity compared to other surfaces. Furthermore, the conclusions obtained by analyzing the excess energy are consistent with the results of the N-N bond length and bond population, band gap, and nitro charge. Therefore, we conclude that the friction sensitivity of different surfaces of EDNA can be evaluated using excess energy.