This paper attempts to simulate fatigue in human arm muscles by modeling their basic building blocks - the motor units. Human muscles can be considered to consist of 3 types of motor units: slow-twitch, fatigue-resistant (S); fast-twitch, fatigue-resistant (FR); and fast-twitch, fatigable (FF) motor units. The S units typically generate the smallest forces that can be maintained almost indefinitely. FR units are capable of generating higher forces more rapidly, but can still maintain force for some time and hence, are generally considered as fatigue-resistant. The FF units are able to generate the highest force, but can only sustain it for a short period of time, making them fatigue-susceptible. Whole muscle force and force fatigue has been modeled by a system of coupled differential equations first proposed by Wexler, et al in 1998, and have been refined by Ding and colleagues since then. These equations are theorized to represent the interaction of the calcium kinetics in the sarcoplasmic reticulum with a mechanical force generator and a coefficient-relaxor in order to capture the decline in the muscle force over time. The decline in the force generation with continued activation (e.g. fatigue) may be due to a complex combination of factors, including a decrease in the sensitivity of the troponin complex to calcium ions. This paper extends the basic whole muscle fatigue model proposed by Ding and colleagues to individual motor units, enabling separate decay coefficients for each motor unit. This approach may make generalizing the muscle model to a variety of muscles possible, versus the current methodology of parameterizing the model to each individual. The model represents activation of the 3 motor units, grouped in bundles of varying proportions that constitute a particular muscle in the human body, to produce a net force for each muscle. This analysis involves the determination of force-time histories of the three elbow flexor muscles, biceps brachii, brachialis and brachioradialis, during tasks involving torque generation. Qualitative comparisons to human torque generation demonstrate that overall elbow flexion torque predictions decay appropriately using this new modeling methodology.