Detailed models of binary branching arterial trees can be generated on a computer by using a new optimization technique; additional branches are successively added, while given conditions of perfusion pressure, total flow and terminal pressure are fulfilled. The vessel radii at each branching obey certain bifurcation laws, and the process of growing the tree is governed by minimizing a target function. The structure thus generated may serve as substrate for the future simulation of haemodynamics in highly detailed arterial trees.