The application of hetero-junction carbon nanotubes (CNTs) is increasing continuously due to their outstanding properties in nano-mechanical systems. Several investigations have been conducted to study the behavior of CNTs. In this paper, straight hetero-junctions and their constituent CNTs (armchair and zigzag) were simulated by a commercial finite element package. Then, the buckling behavior of CNTs was evaluated by comparing the critical buckling load of each straight hetero-junction and its constituent CNTs. Both obtained, i.e. analytical calculations and computational, results were compared. The investigations showed that, first, the behavior of homogeneous CNTs under cantilevered boundary conditions follows the assumption of the classical Euler equation. Second, the analytical solutions are in good agreement with the finite element simulation results. In addition, it was shown that the first critical buckling load of hetero-junctions lies within the value of the fundamental homogeneous CNT range. It was also concluded that the buckling load of straight hetero-junctions and their fundamental CNTs increases by increasing the chiral number of both armchair and zigzag CNTs. The current study provides a better insight towards the prediction of straight hetero-junction CNTs behavior.