Optical flow is the apparent motion of brightness patterns within an image scene. Algorithms used to calculate the optical flow for a sequence of images are useful in a variety of applications, including motion detection and obstacle avoidance. Typical optical flow algorithms are computationally intense and run slowly when implemented in software, which is problematic since many potential applications of the algorithm require real-time calculation in order to be useful. To increase performance of the calculation, optical flow has recently been implemented on FPGA and GPU platforms. These devices are able to process optical flow in real-time, but are generally less accurate than software solutions. For this thesis, two different optical flow algorithms have been implemented to run on a GPU using NVIDIA's CUDA SDK. Previous FPGA implementations of the algorithms exist and are used to make a comparison between the FPGA and GPU devices for the optical flow calculation. The first algorithm calculates optical flow using 3D gradient tensors and is able to process 640x480 images at about 238 frames per second with an average angular error of 12.1 degrees when run on a GeForce 8800 GTX GPU. The second algorithm uses increased smoothing and a ridge regression calculation to produce a more accurate result. It reduces the average angular error by about 2.3x, but the additional computational complexity of the algorithm also reduces the frame rate by about 1.5x. Overall, the GPU outperforms the FPGA in frame rate and accuracy, but requires much more power and is not as flexible. The most significant advantage of the GPU is the reduced design time and effort needed to implement the algorithms, with the FPGA designs requiring 10x to 12x the effort.