Comparison of three third-order upwind differencing schemes is carried out using the driven flow in a squre cavity as the model flow field with the Reynolds numbers as high as 5 000. The schemes considered here are those of (a) Leonard (QUICK), (b) Agarwal and (c) Kawamura and Kuwahara. Evaluation is made with respect to accuracy, stability and the CPU time required. As the result, Leonard's scheme shows the best accuracy of the solution, while there is no significant difference in the CPU time among the schemes. Leonard's scheme also shows the best stability both with fine (61×61) and coarse (21×21) grids; stable solutions for Reynolds numbers up to 5 000 can be obtained by this scheme, while other schemes are unstable for Reynolds numbers above 1 000.