Abstract: A bi-direction evolutionary structural optimization(BESO)method for topology optimization of tunnel support based on a newly developed evolutionary structural optimization(ESO)method is presented.The proposed method can control the number of cavities during the optimization process to avoid the so-called chessboard pattern,and provides two techniques that can overcome oscillate phenomenon.Reinforced rock is considered as artificial reinforcement material,and optimization of tunnel support is transformed into locating the optimal distribution of the reinforcing material.The criteria and sensitivity to prevent floor or sidewall heaves are established,and the optimal support topology of tunnel in homogeneous rock with different situ stresses and with the same reinforcement material are sought for minimum floor or sidewall heaves.The results shows that the floor heaves under optimal designs are much smaller than those under empirical designs and validate the method' s efficiency.