Analyzing antenna coupling is valuable in solving various problems of multi-antenna systems. Through existing studies based on the reaction theorem and infinitesimal dipole modeling (IDM), mutual admittance can be intuitively and efficiently calculated. Extending previous studies based on the reaction theorem and IDM, we propose a method for analyzing mutual admittance between antennas that are located in nonplanar skew positions. There are two main ideas in this paper. The first is IDM extraction using a segmented grid on an antenna computer-aided design (CAD). Using the triangular-meshed antenna CAD, the IDM is extracted on a grid which is equal to the antenna shape. The proposed grid scheme improves the modeling accuracy of the IDM compared to the previous grid schemes. The second idea is to apply a rotation matrix to the IDM for efficient calculation of the coupling of any two antennas with nonplanar skew positions. The strength of the proposed method is that it can predict the mutual coupling between the two antennas by using only independent information for each antenna. However, since only the independent information is used for each antenna, it can reflect only the first-order electromagnetic interaction. Therefore, the proposed method is effective only when the distance between the two antennas is sufficiently far so that the two antennas are regarded independent regardless of the distance variation. Coupling analyses based on these two ideas were performed using two types of antennas in two different cases. The results of the coupling analyses were validated through comparison with the method of moment (MoM) results obtained with the FEKO simulation tool.