Traditional Indian unleavened bread (chapati) was prepared by incorporating wheat bran (insoluble fiber) and oat bran (soluble fiber) at different levels into whole wheat flour. Central composite rotatable design with 2 independent variables (wheat bran and oat bran) at 5 levels (wheat bran 3–9, oat bran 6–12%) was used to design the experiments. The flour samples containing different concentration of bran were analysed for pasting and mixing characteristics. Wheat bran had a negative (p ≤ 0.05) effect on peak viscosity, break down and final viscosity, whereas oat bran had a positive (p ≤ 0.05) effect on set back and final viscosity. Among mixing characteristics, the peak value was negatively affected (p ≤ 0.05) with increase in the level of both variables. Both variables had positive (p ≤ 0.05) effect on hardness of chapati while the cohesiveness, chewiness and overall acceptability scores were negatively affected. Based on compromise optimization, it is recommended to incorporate 5.5 g wheat bran and 9.7 g oat bran per 100 g flour for making optimally acceptable fiber rich chapati.