Carbon　nanotubes　(CNTs)　are　an　excellent　candidate　for　the　reinforcement　of　composite　materials　owing　to　their　distinctive　mechanical　and　electrical　properties.　Reticulate　carbon　nanotubes　(R-CNTs)　with　a　2D　or　3D　configuration　have　been　manufactured　in　which　nonwoven　connected　CNTs　are　homogeneously　distributed　and　connected　with　each　other.　A　composite　reinforced　by　R-CNTs　can　be　fabricated　by　infiltrating　a　polymer　into　the　R-CNT　structure,　which　overcomes　the　inherent　disadvantages　of　the　lack　of　weaving　of　the　CNTs　and　the　low　strength　of　the　interface　between　CNTs　and　the　polymer.　In　this　paper,　a　2D　plane　strain　model　of　a　R-CNT　composite　is　presented　to　investigate　its　micro-deformation　and　effective　stiffness.　Using　the　two-scale　expansion　method,　the　effective　stiffness　coefficients　and　Young＇s　modulus　are　determined.　The　influences　of　microstructural　parameters　on　the　micro-deformation　and　effective　stiffness　of　the　R-CNT　composite　are　studied　to　aid　the　design　of　new　composites　with　optimal　properties.　It　is　shown　that　R-CNT　composites　have　a　strong　microstructure-dependence　and　better　effective　mechanical　properties　than　other　CNT　composites.　Crown　Copyright　(C)　2011　Published　by　Elsevier　Ltd.　All　rights　reserved.