Galaxy Kinematics allow us to gain a better understanding of the formation and evolution of disk galaxies. By utilizing Integral Field Spectroscopy (IFS) we can obtain spatially resolved spectra and investigate galaxy kinematics in great detail. Large IFS surveys of thousands of galaxies are being planned for the coming years and will produce a tremendous amount of data. The currently available computer software for IFS data processing and galaxy kinematic modelling does not take full advantage of the computational strength of the modern hardware, thus making the procedure very time consuming. Our aim is to accelerate kinematic modelling of disk galaxies by exploiting the power of the highly parallel processors available on the Graphics Processing Units (GPUs) and other general purpose computing devices. We explore both grid-based and Markov Chain Monte Carlo (MCMC) methods for parameter estimation and we evaluate the results. For the development of the software the gSTAR supercomputing facility is used.