Bioelastomers are extensively used in biomedical applications due to their desirable mechanical strength, tunable properties, and chemical versatility; however, three-dimensional (3D) printing bioelastomers into microscale structures has proven elusive. Herein, a high throughput omnidirectional printing approach via coaxial extrusion is described that fabricates perfusable elastomeric microtubes of unprecedently small inner diameter (350-550 μm) and wall thickness (40-60 μm). The versatility of this approach is shown through the printing of two different polymeric elastomers, followed by photocrosslinking and removal of the fugitive inner phase. Designed experiments are used to tune the microtube dimensions and stiffness to match that of native ex vivo rat vasculature. This approach affords the fabrication of multiple biomimetic shapes resembling cochlea and kidney glomerulus and affords facile, high-throughput generation of perfusable structures that can be seeded with endothelial cells for biomedical applications. Post-printing laser micromachining is performed to generate micro-sized holes (520 μm) in the tube wall to tune microstructure permeability. Importantly, for organ-on-a-chip applications, the described approach takes only 3.6 min to print microtubes (without microholes) over an entire 96-well plate device, in contrast to comparable hole-free structures that take between 1.5 and 6.5 days to fabricate using a manual 3D stamping approach.