Objective To establish a human elbow joint dynamical modelling in the sagittal plane and seek for an impactful way for solution. Methods To use the optimization toolbox of Matlab for optimizing and solve the modelling. Results The muscle contraction, joint reaction and their corresponding moments were obtained when different external force was applied to the forearm at different elbow joint angle velocity, and it shows that the results are good agree with the literatures. Conclusions The optimization toolbox of Matlab can be used to solve this kind of questions reasonably and the modelling can be used to calculate the muscle contraction, joint reaction and their corresponding moments at the human elbow joint under the application of different external force.