Vascular endothelial growth factor (VEGF) is a powerful regulator of neovascularization. VEGF binding to its cognate receptor, VEGFR2, activates a number of signaling pathways including ERK1/2. Activation of ERK1/2 is experimentally shown to involve sphingosine kinase 1 (SphK1) activation and its calcium-dependent translocation downstream of ERK1/2. Here we construct a rule-based computational model of signaling downstream of VEGFR2, by including SphK1 and calcium positive feedback mechanisms, and investigate their consequences on ERK1/2 activation. The model predicts the existence of VEGF threshold in ERK1/2 activation that can be continuously tuned by cellular concentrations of SphK1 and sphingosine 1 phosphate (S1P). The computer model also predicts powerful effects of perturbations in plasma and ER calcium pump rates and the current through the CRAC channels on ERK1/2 activation dynamics, highlighting the critical role of intracellular calcium in shaping the pERK1/2 signal. The model is then utilized to simulate anti-angiogenic therapeutic interventions targeting VEGFR2-ERK1/2 axis. Simulations indicate that monotherapies that exclusively target VEGFR2 phosphorylation, VEGF, or VEGFR2 are ineffective in shutting down signaling to ERK1/2. By simulating therapeutic strategies that target multiple nodes of the pathway such as Raf and SphK1, we conclude that combination therapy should be much more effective in blocking VEGF signaling to EKR1/2. The model has important implications for interventions that target signaling pathways in angiogenesis relevant to cancer, vascular diseases, and wound healing.