Laminar flow of non-Newtonian shear-thickening fluid through two-dimensional T-channel, was studied numerically using finite volume method. In particular, the effects of Reynolds number over the range of (10 ≤ Re ≤ 600) and power law index (1 ≤ n ≤ 1.8) on the flow characteristics in the bifurcation, have been explored. Streamline plots, the length of recirculation zone and the viscosity variation near the upper and bottom walls of side branch, were presented. The computational results showed that for a particular power-law index, the length of the recirculation zone in the side branch of T-channel, increases gradually with increasing Reynolds number. For a fixed Reynolds number, the length of the recirculation zone in shear-thickening fluids is more higher than the corresponding value in Newtonian case. An exponential relationship to calculate the length of recirculation zone at different values of Reynolds number (Re) and power-law index (n) was established.