It is necessary to use a compression only elements(CO elements) or tension only elements(TO elements) in the structural analysis. Especially, in the case of the structural analysis for Korean traditional wood structures, connections must be modelled by CO or TO elements. In the case of the structural analysis of the culvert structures, CO elements must be used, with the consideration of buoyancy effect. Most commercial computer programs such as SAP2000 and MIDAS/GEN provide these elements. However, since these computer programs only present the concept and the way of using the commands according to respective programs, the basic theories and programming methods can not be understood. Therefore, it is necessary to establish the basic theories and the programming techniques to consider CO elements or TO elements. This study presents the concept and the programming method considering CO elements or TO elements with elasto-plastic stiffness properties, which are the most general nonlinear cases. Basic theories for the consideration of CO elements or TO elements are studied first, where some of possible methods to develop a computer program are investigated. On the basis of these theoretical backgrounds, the most reasonable method and an available algorithm is derived, and then a computer program(sNs) is developed based on the theory and algorithm studied. Lastly, a sample analysis is performed to verify the possibility of the application of sNs.