Twisting and bending characteristics of low-multimode LP21 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 LP21 mode is bending-effect-immune. Experimental testing verifies that the LP21 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 LP21 mode to be highly applicable in fiber specklegram sensors.