—Visual communication design involved with two aspects of visual representation, namely, information and expression. The idea of building a computational model for visual communication design has been developed for many years. However, this objective has only been partially fulfilled as most of the solutions are focused on showing information rather than expression. Lakoff and Johnson have claimed that “human thought processes are largely metaphorical.” Thus, a computational model for visual communication based on the concept of conceptual metaphor is proposed. As brand mark design is considered as a challenging design type that demands the representation of both information and expression, the first attempt of the development of this new model is targeted for this specific type of design. In this paper, the Metaphorical Parametric Model (MPM) is proposed as a computational model to represent brand mark design. The MPM is a type of model which represents the semantic structure rather than the synthetic structure of conceptual components. The components of an MPM is assembled based on the concepts of metaphorical relations which could be signified by spatial relations between the related objects. All objects and relations defined in the MPM are parametrically controllable which could be generated as different visual forms to represent both information and a wide range of metaphorical expressions.