Experimental investigation of the effects of mechanical factors on growth of microvascular networks is hindered by a lack of knowledge of the local mechanics in the vicinity of the vessel sprout. Observations made at the macroscopic scale often indicate a homogeneous stress distribution, but the microenvironment of the endothelial cell may have highly inhomogeneous mechanical behavior. Computational models can potentially provide additional insight into these micromechanical effects that elude experimental studies. The objective of this research was to develop a discrete model to describe angiogenesis in vitro and to study the effects of extracellular matrix (ECM) fiber orientation and initial vessel density. Experimental growth data were gathered from 3D vessel cultures (N=5) imaged on culture days 1-7. Numerical simulations were conducted on a 2D grid, and ECM fiber orientations and local vessel densities were stored at grid nodes. Vessels, represented as discrete segments, were distributed randomly in the domain. Growth occurred via addition of segments to existing vessels, the length of each determined by a growth rate curve fit to experimental data. Growth direction was governed by local ECM orientation and vessel density. Branching occurred stochastically in space, based on a constant that was optimized to match experimental data. Anastomoses were formed when discrete segments intersected or growing tips were in close proximity. Vessel growth off the grid was handled through the use of periodic boundary conditions. Validation was performed through morphometric comparisons of predicted vessel length and branching with experimental data. The discrete angiogenesis model provided a good description of experimentally measured branching and vessel length, with RMS errors of 13% and 1%, respectively. Qualitative comparison of simulated images with confocal data also had good agreement. Future work will couple this discrete model to an existing continuum mechanics model employing the Material Point Method, allowing the replacement of stochastic components of the angiogenesis model by mechanical stimuli. This will provide a framework for predicting the synergistic effects of mechanical factors with angiogenesis.