We present a new theoretical model for analyzing the impact of higher order modes on transverse mode instability in bent Yb-doped fiber amplifiers. The model indicates a comparative analysis of mode instability using the normalized propagation constant in straight and bent fibers amplifiers. The impact of different bending radii, in bent fibers is investigated on the normalized propagation constant. The results are then compared with the straight fibers. Considering all the existed modes, the behavior of mode instability in the fibers with different V-numbers are simulated and explained physically. Manuscript profile