Linear buckling analysis is used to determine critical load factors of a structure and the corresponding buckling mode shapes.  A critical load is obtained by multiplying the initial load by the critical load factor. The significance of the critical load and buckling mode shape is that the structure buckles in the shape of the buckling mode when the critical load exerts on the structure. For instance, if the critical load factor of 5 is obtained from the buckling analysis of a structure subjected to an initial load in the magnitude of 10, this structure would buckle under the load in the magnitude of 50. Note that the buckling analysis has a practical limit since buckling by and large occurs in the state of geometric or material nonlinerity with large displacements.

The analysis is carried out in the following two steps.

1. Linear static analysis is performed under the user-defined loading condition. The geometric stiffness matrices corresponding to individual members are then formulated on the basis of the resulting member forces or stresses.

2. The eigenvalue problem is solved using the geometric and elastic stiffness matrices obtained in Step 1.

The eigenvalues and mode shapes obtained from the above process now become the critical load factors and buckling shapes respectively.