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A concussion, one of the symptoms of brain injury, is often difficult to diagnose using imaging equipment like MRI. Finite element method (FEM) is frequently utilized for head impact problems, and it is also useful to better understand the risks from concussions. In this paper, a constitutive model of the human brain is discussed by elastoplastic theory to simulate the damaging process due to the head collisions that occur in sports such as football and baseball. Specifically, for better diagnosis of concussion, the computational simulation of the head impacts is performed using the FEM. The elastoplastic constitutive equation is applied to the material model of the brain, which was modelled as two spherical layers with an outer elastic skull and inner ductile brain. In this approach, the constitutive equation is primarily verified by varying the hardening modulus in elastoplastic theory. The simulation results show that stress waves generated from the impacts propagate through the head, resulting in complex deformation in a brain region. Since the physical properties of the human brain are difficult to measure directly, they should be validated by varying the physical parameters of the constitutive model to show the reliability improvement of the computational simulations. The validity of the results is based on the evaluation of the hardening modulus by analysing the distribution of the equivalent plastic strain. Consequently, it is shown that a moderate value for the hardening modulus, defined as half the order of its elastic modulus, can be used in the risk assessment of brain concussions.