As a brittle and heterogeneous material, concrete behaves differently under different stress conditions and its bulk strength is loading rate dependent. To a large extent, the varying behavioural properties of concrete can be explained by the mechanical failure processes at a mesoscopic level. The development of a computational mesoscale model in a general finite element environment, as presented in the preceding companion paper (Part 1), makes it possible to investigate into the underlying mechanisms governing the bulk-scale behaviour of concrete under a variety of loading conditions and to characterise the variation in quantitative terms. In this paper, we first present a series of parametric studies on the behaviour of concrete material under quasi-static compression and tension conditions. The loading-face friction effect, the possible influences of the non-homogeneity within the mortar and ITZ phases, and the effect of randomness of coarse aggregates are examined. The mesoscale model is then applied to analyze the dynamic behaviour of concrete under high rate loading conditions. The potential contribution of the mesoscopic heterogeneity towards the generally recognized rate enhancement of the material compressive strength is discussed.