In this article, a Capacity-Centered Integral Software Process Model (CCISPM) applicable to the construction of conventional systems (CS) and of knowledge-based systems (KBS) is described. The model designed is prescriptive, that is, it shows what is done to produce and to maintain an automated solution to a real word problem and who is doing it. It is formalized by applying the object-oriented modeling approach SOCCA (Specifications of Coordinated and Cooperative Activities). This article shows only the formalization of design process, one subprocess taken from several that are involved into the CCISPM. The formal model obtained, which represents all three P: the processes, the products and the people, put together data, process and behavior perspectives into an understandable representation for the software process users (engineer, manager, developer).