In this paper, the non-linear dynamics of a new Shape Memory Alloy (SMA) actuator that possesses impressive payload lifting capabilities are presented. This actuator consists of 48 SMA wires mechanically bundled in parallel forming one powerful muscle. It was designed to lift up to 100 lbs., which is approximately 300 times its weight. This SMA actuator was tested in open loop experiments with different loads and different inputs, such as step, ramp, sinusoid, and half sinusoid, and its dynamic characteristics were evaluated. An important observation made during the dynamic analysis was the unpredictability of the actuator’s response when low to moderate voltages are applied. This characteristic strongly suggests chaotic behavior of the actuator, which could potentially cause control difficulties in fine and high accuracy tasks. An investigation into chaos was conducted using time histories, phase plots, and Poincaré maps. As shown in the diagrams presented in this paper, system response to larger input voltages is periodic, whereas lower input voltages produce responses that strongly indicate chaotic behavior.