In this paper, we have reported the study on instability mechanisms of mid-infrared (MIR) quantum-cascade lasers (QCLs) with Fabry--Perot cavity. Both the saturable absorber (SA) and spatial hole burning (SHB) effects have been included in the analysis. We found that the single-mode and multi-mode instabilities can coexist in the quantum-cascade medium. The multi-mode instability has been observed to be similar to the coherent Risken - Nummedal - Graham - Haken (RNGH) instability, and the single-mode instability has been found to be associated with SHB effect. These results are different from those previously reported in the literature. The linear stability analysis is based on the linearization of Maxwell - Bloch formulism. There are two differences between our analysis and that presented in the literature. One difference lies in the treatment of the complex quantities, while the other is the algorithm for decoupling various instability mechanisms. Furthermore, we have also discussed about the effects of the saturable absorber on the two instability mechanisms. The saturable absorber effect can enhance both kinds of instabilities through lowering their instability thresholds, while the effect on the multi-mode instability is predicted to be more significant.