Inflation of viscous magma intrusions in Earth's shallow crust often induces strain and fracturing within heterogeneous host rocks and dome‐shaped ground deformation. Most geodetic models nevertheless consider homogeneous, isotropic, and linear‐elastic media wherein stress patterns indicate the potential for failure, but without simulating actual fracturing. We present a two‐dimensional Discrete Element Method (DEM) application to simulate magma recharge in a pre‐existing laccolith intrusion. In DEM models, fractures can propagate during simulations. We systematically investigate the effect of the host rock toughness (resistance to fracturing), stiffness (resistance to deformation) and the intrusion depth, on intrusion‐induced stress, strain, displacement and spatial fracture distribution. Our results show that the spatial fracture distribution varies between two end‐members: (a) for high stiffness or low toughness host rock or a shallow intrusion: extensive cracking, multiple vertical surface fractures propagating downward and two inward‐dipping highly cracked shear zones that connect the intrusion tip with the surface; and (b) for low stiffness or high toughness host rock or a deeper intrusion: limited cracking, one central vertical fracture initiated at the surface, and two inward‐dipping fractures at the intrusion tips. Abrupt increases in surface displacement magnitude occur in response to fracturing, even at constant magma injection rates. Our modeling application provides a novel approach to considering host rock mechanical strength and fracturing during viscous magma intrusion and associated dome‐shaped ground deformation, with important implications for interpreting geodetic signals at active volcanoes and the exploitation of geothermal reservoirs and mineral deposits.