Detailed morphological data of vascular smooth muscle cells (VSMC) of coronary arteries were limited. The present study was to quantify dimensions and orientation of swine coronary VSMC and to develop a micro-structural constitutive model of active media. It was found that geometrical parameters of VSMC (length, width, spatial aspect ratio, and orientation) follow normal distributions, and VSMCs orientate towards the circumferential direction of vessels with oblique and symmetrical angles. A micro-structural model of media layer was developed to accurately predict biaxial active responses of coronary arterial media, based on experimental measurements. The present morphological data base and micro-structural model lead to a better understanding of biomechanics of muscular vessels.