An important index for evaluating structural anti-progressive collapse capability is robustness. In order to study the dynamic analysis method of structural robustness, theoretical analysis, numerical simulation, and the destructive model test are conducted. Using samples of a planar cantilever truss and hexagonal star-type dome, the robustness of a truss structure is analyzed on the basis of the strain energy sensitivity method. The influences of structural strain energy and strain energy sensitivity on the structural destructive characteristic are discussed based on the element removal method, which is compared with the stress ratio evaluation method of structural robustness. The results show that the strain energy sensitivity method is effective in reflecting robustness changes of the truss structure, predicting the structural maximum stable bearing loading, recognizing the structural damage mode, and evaluating element vulnerability. Although supporting compression struts and circumferential tension struts have less influence on strain energy sensitivity compared with the radial direction compression bars, they will cause structural integral collapse and strength failure of central compressive struts. As a result, structural robustness evaluation can be achieved by the strain energy method based on analyzing the import coefficient of elements and recognizing the structural damage mode in engineering applications.