Abstract: It is often necessary to implement geosynthetics to reduce risk of sinkhole for roadbed engineering in karst areas, while the theory for design and analysis is far behind the engineering practices. Firstly, the load on the reinforcement is analyzed, and the Terzaghi's arch theory is introduced to calculate the load above sinkhole. The reinforcement is considered composing of three portions which are portion above sinkhole, changeover portion and anchored portion adjacent to sinikhole according to various loading transfer behaviors. The relationship between tension and displacement at the edge of cavity is deduced for the portion above sinkhole. The tension loss is obtained by introducing the Coulumb's law for the changeover portion. The anchored portion is divided into elastic and plastic sections to be solved, and the analytical solution and length of plastic section are deduced by taking the anchored portion as finite or infinite length. Then, a method is proposed to solve the problem by cross of curves. The proposed method is applied in analyzing pull-out tests and full-scale tests. The results shows that the calculated results agree with the measured ones.