White dwarf stars offer a fascinating insight into extrasolar planetary systems. They are the end state for the evolution of most stars, and changes to the star as it evolves can be significant for the dynamics of any orbiting planets. Planetesimals can be accreted onto the white dwarf when their orbits are destabilised following loss of mass from the star as it becomes a white dwarf, and this accretion can be measured through spectroscopic detection of the accreted material. In this project I use computer simulations to model the destabilisation of planetesimals around evolving stars.