Abstract: The critical characteristics of flow transitions refer to the changes of flow state and physical characteristics caused by flow bifurcations. It fundamentally determines the physical laws of flow evolution mode and flow characteristics and is of great significance to reveal the formation mechanism of flow phenomena. In the present paper, the numerical simulations and stability analysis of the classic lid-driven cavity flow with multiple aspect ratios ( R \in 0.1,2.0 ) were performed. We predicted the critical Reynolds numbers for Hopf, Neimark-Sacker and period-doubling bifurcations and the initiation of turbulence. We found that some flows followed the classical Ruelle-Takens model as a routine, while others jumped from periodic flow to turbulent flow due to the period-doubling bifurcation. The mechanism of various flow phenomena was revealed and discussed, such as the loss of stability of flow field, energy cascade and flow topology changing along with aspect ratio etc.. The results are of great significance to reveal the influence of the aspect ratio R on the critical characteristics of the transitions in the cavities. It further improves the study of the internal flow. In the present study, some physical characteristics are found, for example, it is found that the Moffatt effect not only exists with sharp corners, but also in the elongated domain; Regardless of the value of R, the initial instability always starts with the appearance of Hopf bifurcation. For the shallow cavities ( R < \text1\text.0 ), as R increases, the critical Reynolds number of Hopf bifurcation decreases, indicating that the stability becomes more and more easily destroyed. For deep cavity ( R > \text1\text.0 ), compared with classical lid-driven square cavity flow ( R = \text1\text.0 ), the stability is more likely to be lost. Stretching along the longitudinal geometry is not a mandatory constraint to improve the stability of the flow field.