Abstarct: In recent years, use of Graphic Processor Units (GPU) as a parallel processor and accelerator to scientific calculations has been growing up. This type of parallel processing has found a special place in computational fluid dynamics (CFD). Researchers simulate many engineering and natural phenomena with the aid of graphic processors and gained considerable speed up. In this research, two parallel algorithms for solving tri-diagonal system of equations, Cyclic Reduction (CR) and Parallel Cyclic Reduction (PCR) are employed and a different strategy is proposed to solve such system of equations. This approach is called parallel Thomas approach. Lid-Driven cavity problem is used to assessment these parallel algorithms. This problem was simulated by using Thomas algorithm that run on Central Processing Unit (CPU) as well. Runtimes and physical parameters of parallel algorithms, parallel Thomas approach and Thomas algorithm were compared. The maximum speed up of CR, PCR and parallel Thomas approach against CPU runtime was about 4.4x, 5.2x and 38.5x respectively. In this thesis the effect of coalesced memory access and uncoalesced memory access to global memory was studied too, and a 2x speed up achieved in coalesced memory access on GPU. In other hand Parallel Thomas Algorithm can be implemented on transient problems. Many approaches exists which with discretizing equations led to Tri-Diagonal system of equations, for example Alternating Direction Implicit(ADI) method. To assess Parallel Thomas Algorithm performance in time dependent problems, flow over a square considered which with implementing PTA, speed up about 9x achieved.