Functional endothelialized networks constitute a critical building block for vascularized replacement tissues, organ assist devices, and laboratory tools for in vitro discovery and evaluation of new therapeutic compounds. Progress towards realization of these functional artificial vasculatures has been gated by limitations associated with the mechanical and surface chemical properties of commonly used microfluidic substrate materials and by the geometry of the microchannels produced using conventional fabrication techniques. Here we report on a method for constructing microvascular networks from polystyrene substrates commonly used for tissue culture, built with circular cross-sections and smooth transitions at bifurcations. Silicon master molds are constructed using an electroplating process that results in semi-circular channel cross-sections with smoothly varying radii. These master molds are used to emboss polystyrene sheets which are then joined to form closed bifurcated channel networks with circular cross-sections. The mechanical and surface chemical properties of these polystyrene microvascular network structures enable culture of endothelial cells along the inner lumen. Endothelial cell viability was assessed, documenting nearly confluent monolayers within 3D microfabricated channel networks with rounded cross-sections.