A new computer program, LATIS, being developed at Lawrence Livermore National Laboratory is used to study the effect of pulsed laser irradiation with temperature feedback on endovascular patch welding. Various physical and biophysical effects are included in these simulations: laser light scattering and absorption, tissue heating and heat conduction, vascular cooling, and tissue thermal damage. The geometry of a patch being held against the inner vessel wall (500 micrometer inner diameter) by a balloon is considered. The system is exposed to light pulsed from an optical fiber inside the balloon. The laser power is adjusted during the course of a pulse. This is done automatically in the simulation by temperature feedback. A minimum in the depth of damage into the vessel wall is found. The minimum damage zone is about the thickness of the patch material that is heated by the laser. The more ordered the tissue the thinner the minimum zone of damage. The pulse length which minimizes the zone of damage is found to be the time for energy to diffuse across the layer. The delay time between the pulses is determined by the time for the heated layer to cool down. An optimal pulse length exists which minimizes the total time needed to weld the patch to the wall while keeping the thickness of the damaged tissue to less than 100 micrometers. For the case that is considered, a patch dyed with light absorbing ICG on the side next to the vessel (thickness of the dyed layer is 60 micrometer), the best protocol is found to be 33 - 600 ms pulses applied over 1.6 min.