Abstract: The CERN Large Hadron Collider (LHC) is designed to collide proton beams of unprecedented energy, in order to extend the frontiers of high-energy particle physics. During the first very successful running period in 2010-2013, the LHC was routinely storing protons at 3.5-4 TeV with a total beam energy of up to 146 MJ, and even higher stored energies are foreseen in the future. This puts extraordinary demands on the control of beam losses. An uncontrolled loss of even a tiny fraction of the beam could cause a superconducting magnet to undergo a transition into a normal-conducting state, or in the worst case cause material damage. Hence a multistage collimation system has been installed in order to safely intercept high-amplitude beam protons before they are lost elsewhere. To guarantee adequate protection from the collimators, a detailed theoretical understanding is needed. This article presents results of numerical simulations of the distribution of beam losses around the LHC that have leaked out of the collimation system. The studies include tracking of protons through the fields of more than 5000 magnets in the 27 km LHC ring over hundreds of revolutions, and Monte Carlo simulations of particle-matter interactions both in collimators and machine elements being hit by escaping particles. The simulation results agree typically within a factor 2 with measurements of beam loss distributions from the previous LHC run. Considering the complex simulation, which must account for a very large number of unknown imperfections, and in view of the total losses around the ring spanning over 7 orders of magnitude, we consider this an excellent agreement. Our results give confidence in the simulation tools, which are used also for the design of future accelerators.