Palm vein-based biometric highlights its contactless acquisition, high precision, and user acceptance. However, the lack of publicly available databases with a large number of individuals challenges the continuous growth of this biometrics. In this context, the generation of synthetic images offers a promising solution to address this limitation and facilitate the evaluation of recognition algorithms. This paper introduces a geometric model for generating realistic synthetic palm vein images for the creation of large-scale databases without collecting personal information. The model parameters were obtained by characterizing the external and internal structures of the palm, enabling the description of the vascular networks using their most representative points. Generated intermediate points are connected using piecewise interpolation to derive the vascular network structure. We applied biological optimization principles based on Murray’s law to calculate the network thickness. The vascular structure was fused with generated palmprint texture to obtain the final synthetic palm vein image. An extensive evaluation examines the similarity between real and synthetic samples using qualitative and quantitative metrics. The results show the effectiveness of our approach in generating realistic synthetic palm vein images; thereby, the proposed model can be used to develop large-scale datasets.