The outstanding properties of carbon nanotubes (CNTs) keep attracting the attention of researchers from different fields. CNTs are promising candidates for applications e.g. in lightweight construction but also in electronics, medicine and many more. The basis for the realization of the manifold applications is a detailed knowledge of the material properties of the carbon nanotubes. In particular for applications in lightweight constructions or in composites, the knowledge of the mechanical behavior of the CNTs is of vital interest. Hence, a lot of effort is put into the experimental and theoretical determination of the mechanical material properties of CNTs. Due to their small size, special techniques have to be applied. In this research, a modified molecular structural mechanics model for the numerical determination of the mechanical behavior of carbon nanotubes is presented. It uses an advanced approach for the geometrical representation of the CNT structure while the covalent bonds in the CNTs are represented by beam elements. Furthermore, the model is specifically designed to overcome major drawbacks in existing molecular structural mechanics models. This includes energetic consistency with the underlying chemical force field. The model is developed further to enable the application of a more advanced chemical force field representation. The developed model is able to predict, inter alia, the lateral and radial stiffness properties of the CNTs. The results for the lateral stiffness are given and discussed in order to emphasize the progress made with the presented approach.