Vector Fitting (VF) algorithm has been widely used for system identification from multiport tabulated data. Particularly, it is of high interest to the design community focused on modeling of high-speed modules such as large number of coupled interconnects, packaging structures and variety of electromagnetic modules. Since VF and strategies based on it require many iterations to arrive at optimal number of converged poles, it is highly desired to reduce the computational cost of each VF iteration. This thesis advances the applicability of VF to exploit the emerging massively parallel graphical processing Units (GPUs). Necessary parallelization strategies suitable for GPU platforms are developed. For large problem sizes (increasing number of poles and ports). Numerical results demonstrate that the proposed method provides significant speedup compared to both the multi-CPU based VF as well as the existing GPU based parallel VF techniques.