Beam Delivery Simulation (BDSIM) is a program that simulates the passage of particles in a particle accelerator. It uses a suite of standard high energy physics codes (Geant4, ROOT and CLHEP) to create a computational model of a particle accelerator that combines accurate accelerator tracking routines with all of the physics processes of particles in Geant4. This unique combination permits radiation and detector background simulations in accelerators where both accurate tracking of all particles is required over long range or over many revolutions of a circular machine, as well as interaction with the material of the accelerator.