Phase analysis techniques of fringe patterns have been widely used for noncontact three-dimensional shape and deformation measurement by the fringe projection method. Recently, we developed two novel accurate phase analysis methods. One is the two-dimensional sampling moire method to perform robust phase analysis for a single-shot fringe pattern. The other is the two-dimensional spatiotemporal phase-shifting method to analyze phase distribution accurately for multi-step phase-shifted fringe patterns. To perform accurate phase analysis under low signal-to-noise ratio conditions, both the above two methods use the two-dimensional discrete Fourier transform or fast Fourier transform. Therefore, these algorithms are computationally expensive compared with the conventional one-dimensional sampling moire and phase-shifting methods. In this study, a fast parallelization implementation for two-dimensional phase-shifting methods, including the two-dimensional sampling moire method and the spatiotemporal phase-shifting method, are presented by utilizing multi-core CPU. Simulation and experimental results demonstrate that phase analysis can reach 7.5 and 5.9 times faster by use of a 12-core CPU compared with a single CPU.