We present a computational model and analysis of the dynamic behavior of epidermal growth factor receptor (EGFR) signaling in cardiac muscle tissue, with the aim of exploring transduction of mechanical loading into cellular signaling that could lead to cardiac hypertrophy. For this purpose, we integrated recently introduced models for ligand dynamics within compliant intercellular spaces and for the spatial dynamics of intracellular signaling with a positive feedback autocrine circuit. These kinetic models are here considered in the setting of a tissue consisting of cardiomyocytes and blood capillaries as a structural model for the myocardium. We show that autocrine EGFR signaling can be induced directly by mechanical deformation of the tissue and demonstrate the possibility of self-organization of signaling that is anisotropic on the tissue level and can reflect anisotropy of the mechanical deformation. These predictions point to the potential capabilities of the EGFR autocrine signaling circuit in mechanotransduction and suggest a new perspective on the cardiac hypertrophic response.