One of the crucial issues for developing computer aided conceptual design system is representation of functions which represent designers’ intention. Representing functions is also crucial not only for representing design objects but also for describing conceptual design processes, in which designers operate mainly functional concepts. Namely, function is a key concept to integrate object modeling and process modeling in design. In this paper, first we extend the FBS (Function-Behavior-State) diagram, which we have already proposed, by introducing three additional concepts for representing a function; namely, function body that represents designers’ intention directly, function modifier that qualifies a function body, and objective entity on which the function body occurs. This extended FBS diagram, called FBS/m (modifier) diagram, enables us to represent designers’ intention more precisely than the original FBS diagram. Then, we propose an FEP (Functional Evolution Process) model to represent design processes. In the FEP model, the FBS model of a design object is evolved through three steps, i.e., functional actualization, functional evaluation and functional operation. Functional actualization depicts a process to obtain physical descriptions from functional description. Functional evaluation is a process to measure realizability of functions of the design object. Functional operation is a process to operate functions to improve the design. Based on the FEP model, we analyze an actual design process, and show that the FEP model is suitable for representing designers’ intention along with design processes.