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The increasing interest in micro-electromechanical systems (MEMS) has raised the requirement for novel composite materials with improved material properties. A direct modeling strategy for the prediction of the effective moduli of composite materials based on finite element method (FEM) is investigated in this paper. A specimen model in FEM is firstly meshed into small indiscriminating domains, which then are assigned with quasi-random material labels to distinguish different component phases of the composite. This meshed composite model with random component phase distribution is ready to be solved by ordinary FEM under proper boundary conditions and loading scheme. As an illustration, the effective Young's modulus (E) and Poisson's ratio (v) of such composites model with glass and epoxy components are computed under the plane stress and strain configurations. The sensitivity of initial domain numbers and refinement levels on the prediction is investigated. Well known Hashin-Shrikman bounds and GSCM predictions are retrospected for validation and comparison purpose. The predictions under plane stress configuration are found to be more stable than its counterpart and the first level of refinement can provide reasonable results.