Organ printing is a robotic computer-aided layer by layer additive biofabrication of 3D tissue and organ constructs using tissue spheroids as building blocks. It has been demonstrated that intraorgan branched vascular tree could be bioprinted inside 3D tissue and organ constructs. However, maturation of built-in branched vascular tree suitable for perfusion needs some time. In order to buy time necessary for maturation of branched vascular tree and maintain viability of bioprinted 3D tissue constructs an interstitial perfusion with special irrigation dripping bioreactor could be used. Computational simulations with using Surface Evolver software and Computational Fluid Dynamics software demonstrated that short term viability of bioprinted 3D tissue and organ constructs by interstitial flow is feasible.