Purpose: In the context of analyzing neck vascular morphology, this work formulates and compares Mask R-CNN and U-Net-based algorithms to automatically segment the carotid artery (CA) and internal jugular vein (IJV) from transverse neck ultrasound (US). Methods: US scans of the neck vasculature were collected to produce a dataset of 2439 images and their respective manual segmentations. Fourfold cross-validation was employed to train and evaluate Mask RCNN and U-Net models. The U-Net algorithm includes a post-processing step that selects the largest connected segmentation for each class. A Mask R-CNN-based vascular reconstruction pipeline was validated by performing a surface-to-surface distance comparison between US and CT reconstructions from the same patient. Results: The average CA and IJV Dice scores produced by the Mask R-CNN across the evaluation data from all four sets were 0.90 ± 0.08 and 0.88 ± 0.14. The average Dice scores produced by the post-processed U-Net were 0.81 ± 0.21 and 0.71 ± 0.23 , for the CA and IJV, respectively. The reconstruction algorithm utilizing the Mask R-CNN was capable of producing accurate 3D reconstructions with majority of US reconstruction surface points being within 2 mm of the CT equivalent. Conclusions: On average, the Mask R-CNN produced more accurate vascular segmentations compared to U-Net. The Mask R-CNN models were used to produce 3D reconstructed vasculature with a similar accuracy to that of a manually segmented CT scan. This implementation of the Mask R-CNN network enables automatic analysis of the neck vasculature and facilitates 3D vascular reconstruction.