In the distributed and horizontally integrated manufacturing environment found in agile manufacturing, there is a great demand for new product development methods that are capable of generating new customized assembly designs based on mature component designs that might be dispersed at geographically distributed partner sites. To cater for this demand, this paper addresses the methodology for complex assembly variant design in agile manufacturing. It consists in fundamental research in two parts: (i) assembly modeling; and (ii) assembly variant design methodology. This paper, the first of a two-part series, presents the assembly variant design system architecture and the assembly modeling methodology. First, a complementary assembly modeling concept is proposed with two kinds of assembly models, the hierarchical assembly model and the relational assembly model. The first explicitly captures the hierarchical and functional relationships between constituent components whereas the second explicitly captures the mating relationships at the form-feature-level. These models are complementary in the sense that each of them models only a specific aspect of assembly-related information but together they include the required assembly-related information. They are further specialized to accommodate the features of assembly variant design. As a result, two kinds of assembly models, the assembly variants model and the assembly mating graph are generated. These assembly models serve as the basis for assembly variant design which is discussed in the companion paper.