Shock and impact loading often generates stress waves in the responding structural object with a drastic time and spatial variation. Consequently the transient response of the material involves not only high strain rate, but also a highly non-homogeneous stress field with respect to the mesoscale heterogeneity of the concrete-like materials. To comprehensively capture the material response and the underlying mechanisms under such loading conditions, the use of a mesoscale model is desirable. This paper discusses the development of a mesoscale model that describes reasonably the random mesoscopic structure of concrete materials and at the same time allows for the simulation of response under complex dynamic loads. Due to the complexity in the generation and meshing of the random aggregate structure of concrete, at the present stage the random mesoscale geometry is generated within a 2D plane. The use of a 2D representation of a concrete is common and may be acceptable in lower loading rate applications, however, under high rate loading a 2D model for concrete in compression could introduce noticeable errors due to an inability to fully capture the crucial lateral inertia confining effect. This special phenomenon is investigated in this paper, and a remedial modelling scheme is proposed to minimize the inaccuracy in a 2D mesoscale model for high strain rate loading. Finally, the experimentally observed strain rate increase factor is discussed in light of the mesoscale numerical modeling results.