Epoxy polymer concrete (EPC) has high volume fraction of aggregate and extraordinary mismatch of mechanical properties between the granite aggregate and the epoxy matrix, which make the mesoscale modeling a challenging issue. This paper demonstrates how the mesoscale model of EPC is generated and employed to investigate the mechanical responses of EPC under tension and bending. By introducing rotation operation into take-and-place procedure, high aggregate volume fraction (over 75%) of irregular shaped aggregate can be achieved efficiently following various practical gradations. Based on the obtained geometrical model, a three-phase model consisting of aggregate, matrix, and interfacial transition zone (ITZ) is constructed, in which the ITZ is defined as stiff as the granite aggregate and as strong as the epoxy matrix to coordinate the deformation of the other two phases in EPC. The proposed model demonstrates good performance in finite element analysis to explore the stress–strain relation and damage development of EPC during tensile deformation.