For the reliability based aerodynamic shape design optimization, many computing efforts are required and it is almost impossible to perform with the general direct optimization methods. To overcome this computational limitation, the two-point approximation method(TPA) is adapted that uses the function values and the sensitivities already known from the optimization procedure and can consider the reliability without additional calculations. The conventional TPAs show good approximations for many cases but sometimes give inaccurate or unstable. To improve on these shortcomings, the bi-directional two-point approximation method(BTPA) is proposed. Through the combination of BTPA and the adjoint sensitivity analysis, an aircraft wing shape design optimization in 3-dimensional viscous flows is performed.