The stability of surrounding rock support structure is the key to the design of underground structure. To overcome the insufficiency of statistical information on surrounding rock parameters of deep tunnels

the information-gap theory is introduced to develop a non-probabilistic reliability analysis method for surrounding rock. The info-gap model of dimensionless parameters is given based on the uncertainty level

and the robust function of reliability analysis is obtained according to the system model and performance requirements. The maximum fluctuation amplitude of uncertainty parameter which can be tolerated before structural failure is taken as a robust reliability index. An optimal support resistance of homogeneous elastoplastic surrounding rock is obtained based on the slip-line field theory. Then a response function of stability analysis of surrounding rock support structure is established. The engineering example illustrates the specific operation procedures of robust reliability analysis. The parameter analysis shows that the greater the support resistance is

the more stable the structure is. In the meanwhile

it is shown that increasing the internal friction angle and cohesion of the surrounding rock is the key to improve the stability of the support structure. The proposed procedure is a reasonable and effective method to deal with the uncertain problem when the parameter information and sample data are limited.