Critical Bucking Load (CBL) is one of the essential parameters to describe the mechanic stabilities of materials, e.g. the low-dimensional carbon nanostructures. While the CBL of pristine carbon nanotubes have been previously investigated using the quantum mechanics-based calculations, the effect of geometrical variation on the CBL of carbon nanomaterials is rarely reported since it need considerably large atomic models, which needs high computational cost. In this study, both the analytical and Finite Element (FE) methods were employed to systematically explore the impact of atomic vacancies, shapes and heterostructures on the CBLs of carbon nanomaterials with the acceptable computational cost. Our studies on the pristine CNTs first demonstrate the validity of the method we used. After that, the systems with mono-/bi-/tri-/pinole-vacancies either on nanocones, nanotube, linearly-joined nanotubes or angle-adjoined were simulated and analyzed. Our results reveal that the CBL values decrease with the increase of the aspect ratio of all considered nanomaterials. Based on the obtained results, the CBL of nanocone with the aspect ratio of 1, reduces significantly, from 50 nN to 10 nN when the aspect ratio is 3. The CBL of homogeneous, capped, and joint CNTs reduces to below 2 nN when the aspect ratio is above 14. The introduction of geometric variations can greatly affect the CBL values. The larger atomic vacancy has more serious impact on the CBLs. The most highlighted impact is for the pinhole vacancy where the CBL reduces to up to 70% of the original value. Our studies on linearly-joint and angle-joint carbon hybrids further demonstrate that the CBL can also be affected by the boundary conditions and joint structures of the hybrids.