Abstract An accurate model of the human upper limb is crucial for various applications, including prosthetic development, optimizing ergonomics, and rehabilitation. The novelty of this research is to obtain a model that predicts the forces of muscles, ligaments, and joint reactions under any loading conditions, thereby enabling the prediction of musculoskeletal forces during different daily activities. For this, a multibody three-dimensional dynamic model of the human upper limb is presented to study the upper limb musculoskeletal system. The model comprises 35 muscle elements, 11 ligaments, and 7 joints. Thirty equations of motion with 73 unknowns were obtained using Newton’s second law of motion. The Ariel Performance Analysis System (APAS) was utilized to record and analyze the motion of 16 bony landmarks using 8 digital video cameras with a sampling rate of 100 frames per second. The genetic algorithm (GA) and particle swarm optimization (PSO) are used to solve the redundant force problem of the model. The GA and PSO are implemented with two distinct objective functions; the first is the sum of the squared muscles’ stresses. The second one is the sum of the muscles’ energy consumption. The model was validated through EMG recordings of eight superficial muscles and with the available data in the literature. The results show that the inclusion of the ligaments at the GH and elbow joints in addition to the trapezoid and conoid ligaments in the model led to a more precise prediction of the muscles’ force. The PSO shows more accuracy and smoothness of the predicted muscles’ force, despite the GA taking more running time and requiring significant memory resources. The model also revealed that there is no great difference in the predicted muscles’ force when using any of the two cost functions.