Twisting and bending characteristics of low-multimode ${\mathrm{LP}}_{21}$ mode propagation in optical fibers is presented for the first time. Theoretical fiber mode modeling, combining geometrical rotation with opto-elastic effects, demonstrates that the propagation of the ${\mathrm{LP}}_{21}$ mode is bending-effect-immune. Experimental testing verifies that the ${\mathrm{LP}}_{21}$ mode specklegram rotates 0.9112 of the fiber twist angle in a fused silica fiber, independent of any fiber bending. This characteristic allows for the ${\mathrm{LP}}_{21}$ mode to be highly applicable in fiber specklegram sensors.