Technology of deployable space structures is necessary for spacecraft to challenge advanced missions. It is important in designing the deployable space structures that they are easily deployable and reliably repeatable. Traditional approach for improving the repeatability was conducted by investigating errors and its effect to the deployment. However, the traditional approach has a problem that results change depending on estimation of the errors. With that background, this study proposes numerical methods to enable selection of robust deployable structures against the errors. The repeatability is decreased due to occurrence of the buckling caused by the errors. Therefore, a structure not occurring the buckling should be selected for designing of a reliably repeatable structure. The buckling is detected by non-positive eigenvalues of a stiffness matrix of the structure in static analysis. However, detection of the buckling in dynamic analysis is difficult because the eigenvalue is also non-positive when the structure has rigid-body motion. This study solved the problem by proposing a method to discriminate the buckling from the rigid-body motion. Furthermore, a method to evaluate instability of the structure quantitatively is desired when only structures occurring the buckling are available for the spacecraft. When the buckling occurs, small disturbance sets off grave displacement. Therefore, this study proposed the method to evaluate the instability quantitatively by calculating disturbance force and buckling displacement as index values of the instability based on the equation of motion. Finally, it was confirmed that the proposed methods are appropriate by the dynamic analyses of truss arch.