Micromechanical modeling analyses have been carried out to enhance our understanding of the effects of heterogeneity on the failure phenomenon in brittle rock. Uniaxial tension tests have been numerically simulated using the Dynamic Lattice Network Model. Micromechanical properties in test specimens are assumed to vary spatially following the Weibull distribution. The test results obtained in unnotched and notched specimens show that strain localizations occur around the crack tips, leading to local fracture developments, and resulting in global failure. The results also suggest that the distribution of material heterogeneity affects the development of the fracture process zone.