Beam Delivery Simulation (BDSIM) is a C++ program that utilises the Geant4 toolkit to simulate both the transport of particles in an accelerator and their interaction with the accelerator material. BDSIM is capable of simulating a wide variety of accelerator components and magnets with Geant4 geometry dynamically built based on a text input file. Thick lens accelerator tracking routines are provided for fast accurate tracking in a vacuum.