Extensive experimental studies have identified vascular endothelial growth factor (VEGF) concentrations and concentration gradients as major factors in angiogenesis; however, localized in vivo measurements of these parameters have not been possible. We have developed a three-dimensional computational model of skeletal muscle fibers, blood vessels and interstitial space. Here it is applied to rat extensor digitorum longus. VEGF isoforms are secreted by myocytes, diffuse through extracellular matrix and basement membranes, and bind endothelial cell surface receptors on blood vessels. In addition, one isoform, VEGF₁₆₄, binds to proteoglycans in the interstitial space. VEGF secretion rate is determined from the predicted tissue oxygen level through its effect on the HIF-1 transcription factor. We estimate VEGF secretion, its concentrations and gradients in resting muscle and for different levels of exercise. The effects of low levels of inspired oxygen are also studied. We predict that the high spatial heterogeneity of muscle fiber VEGF secretion in hypoxic tissue leads to significant gradients of VEGF concentration and VEGF receptor activation. VEGF concentration gradients are predicted to be significant both in resting and exercising muscle (4% and 6-8% change in VEGF over 10µm, respectively), sufficient for chemotactic guidance of 50µm-long sprout tip cells. VEGF gradients also result in heterogeneity in VEGF receptor activation - a possible explanation for the stochasticity of sprout location. In the absence of interstitial flow, gradients are 10-fold steeper in the transverse direction (i.e. perpendicular to the muscle fibers) than in the longitudinal direction. This may explain observed perpendicular anastomoses in skeletal muscle.