<p>A structural geological model is an important basis for the understanding of subsurface structures and exploration of mineral resources, especially petroleum reservoirs. In the field of geological modelling, the lack of a well-defined semantic level description and corresponding computer characterization method hinders its application. In this paper, we propose the semantic descriptions for structural geological models in order to facilitate computer based processing of geological semantics. A multi-level heterogeneous network is proposed to characterize the semantic description for this purpose. The semantic description of a structural geological model gives a complete description of structural units (called semantic entities) of structural models. Basic semantic entities include points, lines, interfaces, bodies, formations and advanced semantic entities include stratified structures/massive structures, planar structures, linear structures. Semantic relations represent the logical relationships among these semantic entities. The multi-level heterogeneous network contains complete information of structural geological models for both geometry and geology. Hence, it has a one-to-one correspondence with a structural geological model. In particular, we propose a bottom-up and top-down integrating structural modelling method based on semantic descriptions. This approach aims to address defects of the existing structural modelling methods that can only carry out bottom-up modelling. Because the addition of semantic information, it improves the adaptability of structural modelling to complex structures and enhances modelling efficiency.</p>