Effective Poisson's ratios of two model polymer networks with special types of microstructures which are randomly oriented have been numerically evaluated. The results, having been graphically represented, show the micromechanical condition under which these networks exhibil negative Poisson's ratios. thus being of great importance in aiding experimental synthesis of such liquid-crystal-like polymer networks in which stretchable and bendable rodlike molecular segments (arms and backbones) meet at rigid molecular crosslinks (junctions),