In order to improve the capabilities of managing the roof and enduring the load of the standing shield’s hydraulic support, the motion trace of the roof beam endpoint should be approximate twisted pair line, and its maximal horizontal swing value should be minimal. In this paper, the motion characteristics for the fourbar linkage of the hydraulic support were analyzed, and its mathematic model for optimization design was established. The length of each bar and the correspondent parameters were determined by genetic algorithm, when the motion trace of the roof beam endpoint was twisted pair line, and the maximal horizontal swing value e of the roof beam endpoint was minimal. The ZY35 hydraulic support was taken as an example to validate the optimization result. The ideal design parameters of the ZY35 hydraulic support can be obtained based on genetic algorithm, and its working status and support effect is stable and favorable.