Vascular shunt insertion is a fundamental surgical procedure used to temporarily restore blood flow to tissues. It is often performed in the field after major trauma. We formulate a problem of automated vascular shunt insertion and propose a pipeline to perform Automated Vascular Shunt Insertion (AVSI) using a da Vinci Research Kit. The pipeline uses a learned visual model to estimate the locus of the vessel rim, plans a grasp on the rim, and moves to grasp at that point. The first robot gripper then pulls the rim to stretch open the vessel with a dilation motion. The second robot gripper then proceeds to insert a shunt into the vessel phantom (a model of the blood vessel) with a chamfer tilt followed by a screw motion. Results suggest that AVSI achieves a high success rate even with tight tolerances and varying vessel orientations up to 30°. Supplementary material, dataset, videos, and visualizations can be found at https://sites.google.com/berkeley.edu/autolab-avsi.