When bearing external load, geotechnical material will turn from elastic state to plastic state, eventually to destruction state. There is something different between yield situation and failure situation for geotechnical material. The yield situation represents that materials turn elastic state into a plastic state. However, in failure situation, geotechnical materials would get instability. For ideal elastic-plastic materials, stress criterion is difficult to distinguish between the yield and failure, so the limit strain is proposed as a damage criterion for geotechnical material. The solution model and method for the dynamic limit strain are put forward, and the dynamic limit strain is used as a failure criterion, which could express integral damage or local failure of materials under dynamic action. When the local failure surface gets connected, overall destruction would appear. Based on a slope project under earthquake action, the position of initial crack and evolutionary process of the crack at the slope as well as the limit load were got. The limit load calculated by limit strain criterion was in accordance with the results computed by the numerical limit analysis with displacement unconverged criterion (overload method and strength reduction method ), which shows the feasibility of the limit strain criterion in the dynamic analysis.