We present a two-dimensional mesoscopic finite element model for simulating the rate- and moisture-dependent material behavior of concrete. The idealized mesostructure consists of aggregate grains surrounded by an interfacial transition zone embedded in the bulk material. We examine the influence of the most significant constitutive model parameters on global and local response. Different distributions and shapes of the aggregate grains are tested. Three model parameter sets, corresponding to different moisture conditions, are employed in the analysis of two specimens in which the applied loading rate is significantly different. The results indicate that the loading rate has a stronger influence than the saturation level on fracture processes and global strength.