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.