This paper describes an axiomatic functional and object-oriented design framework for co-design and co-analysis of product functions, physical structures, and their mapping relations. This design framework consists of function model, object model, information flow model, and axiomatic design model. These models are constructed level-by-level and side-by-side to form a concurrent and coordinated design paradigm. The components of the resulting design are reviewed by the design team, summarized in a task assignment table, and allocated to respective disciplinary engineers for detail design. This methodology enables mechanical, electronic, and software engineers to collaborate and develop mechatronic products in a concurrent and integrated fashion.