Abstract: A three dimensional microscopic model of the reticulate carbon nanotube/epoxy (R-CNT/EP) composites was established according to its structural characteristics based on the assumption of the uniform distribution of R-CNT. The effective stiffness coefficients and Young's modulus of the R-CNT/EP composite were calculated by two-scale expansion method. It is shown that the mechanical properties of the R-CNT/EP composite are anisotropic and the strength along the direction of the vapor flow is much higher than that in other directions. The shape of the R-CNT plays an important role on the mechanical properties of the R-CNT/EP composite, and the effective stiffnesses and Young's modulus of the R-CNT/EP composites are the highest when the angles of the Y-junctions are equal. All of the effective stiffnesses and Young's modulus of the R-CNT/EP composites are enhanced with the increase of volume fraction of R-CNT, but the influence degrees are different.