In this paper we present a model of computer architecture. The proposed model uses a triplet to describe the static structures of a computing machine; the more dynamic parts of the architecture are modeled as relations between the triplet components. A recursive formalism of the model is developed to facilitate the hierarchical representation of an entire machine’s architecture or the architecture of its components. A simple, but functional, 8-bit microprocessor architecture is used to show how the formalisms of the model may be applied to existing architectures. Two additional applications of the model are presented to describe microprogramming and virtualization.