To relate the mechanical responses of hard-soft copolymer systems with their microstructures, a coarse-grained molecular dynamics approach is employed, and mechanical properties of both hard and soft domains are calculated. We first investigate the enhancement mechanism of hard domains under tensile and shear loading conditions with pressure. The energy factor that denotes the interaction between hard beads dominates the microphase separation and morphology. Our numerical experiments show that pressure is the most crucial factor in shear-under-pressure tests, with larger pressure leading to higher shearing resistance of the copolymers. The viscoelastic behaviors of hard-soft copolymers are computed from the stress autocorrelation function. The stress relaxation indicates that the soft matrix is in a rubbery state at room temperature while hard domains are "glass-like" and can be viewed as elastic solids in a macroscale model. In addition, local elastic constants of hard domains are computed using the stress-strain fluctuation method with purely local stress and local strain. Those results can be used as inputs for macroscale models for copolymers and can provide guidelines for designing polymeric materials. (c) 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 1552-1566