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In this paper, the embedded discontinuity approach is applied in finite element modeling of rock in compression and tension. For this end, a rate-dependent constitutive model based on (strong) embedded displacement discontinuity model is developed to describe the mode I, mode II and mixed mode fracture of rock. The constitutive model describes the bulk material as linear elastic until reaching the elastic limit. Beyond the elastic limit, the rate-dependent exponential softening law governs the evolution of the displacement jump. Rock heterogeneity is incorporated in the present approach by random description of the mineral texture of rock. Moreover, initial microcrack population always present in natural rocks is accounted for as randomly-oriented embedded discontinuities. In the numerical examples, the model properties are extensively studied in uniaxial compression. The effect of loading rate and confining pressure is also tested in the 2D (plane strain) numerical simulations. These simulations demonstrate that the model captures the salient features of rock in confined compression and uniaxial tension. The developed method has the computational efficiency of continuum plasticity models. However, it also has the advantage, over these models, of accounting for the orientation of introduced microcracks. This feature is crucial with respect to the fracture behavior of rock in compression as shown in this paper. [ABSTRACT FROM AUTHOR]