Angiogenesis, the formation of new blood vessels from pre-existing ones, begins during embryonic development and continues throughout life. Sprouting angiogenesis is a well-defined process, being mainly influenced by vascular endothelial growth factor (VEGF). In this study, we propose a meshless-based model capable of mimicking the angiogenic response to several VEGF concentrations. In this model, endothelial cells migrate according to a diffusion-reaction equation, following the VEGF gradient concentration. The chick chorioallantoic membrane (CAM) assay was used to model the branching process and to validate the obtained numerical results. To analyse the angiogenic response, the total vessel number and the total vessel length presented in the CAM images and in the simulations for all the VEGF concentrations tested were quantified. In both the CAM assay and simulation, the treatments with VEGF increased the total vessel number and the total vessel length. The obtained quantitative results were very similar between the two methodologies used. The proposed model accurately simulates the capillary network pattern concerning its structure and morphology, for the lowest VEGF concentration tested. For the highest VEGF concentration, the capillary network predicted by the model was less accurate when compared to the one presented in the CAM assay but this may be explained by changes in blood vessel width at higher VEGF concentrations. This remains to be tested.