Understanding modern particle accelerators requires simulating charged particle transport through the machine elements. These simulations can be very time consuming due to the large number of particles and the need to consider many turns of a circular machine. Stream computing offers an attractive way to dramatically improve the performance of such simulations by calculating the simultaneous transport of many particles using dedicated hardware. Modern Graphics Processing Units (GPUs) are powerful and affordable stream computing devices. The results of simulations of particle transport through the booster-to-storage-ring transfer line of the DIAMOND synchrotron light source using an NVidia GeForce 7900 GPU are compared to the standard transport code MAD. It is found that particle transport calculations are suitable for stream processing and large performance increases are possible. The accuracy and potential speed gains are compared and the prospects for future work in the area are discussed.