Future linear colliders plan to collide polarised beams and the planned physics reach requires knowledge of the state of polarisation as precisely as possible. The polarised beams can undergo depolarisation due to various mechanisms. In order to quantify the uncertainty due to depolarisation, spin tracking simulations in the International Linear Collider (ILC) Beam Delivery System (BDS) and at the Interaction Point (IP) have been performed. Spin tracking in the BDS was achieved using the BMAD subroutine library, and the CAIN program was used to do spin tracking through the beam-beam collision. Assuming initially aligned beamline elements in the BDS, a ground motion model was applied to obtain realistic random misalignments over various time scales.Depolarisation at the level of 0.1% occurs within a day of ground motion at a noisy site. Depolarisation at the IP also exceeds 0.1% for the nominal parameter sets for both the ILC and for the Compact Linear Collider (CLIC).Theoretical work is underway to include radiative corrections in the depolarisation processes and simulation of the depolarisation through the entire collider is envisaged.