Head injury caused by the traffic crash accident is recognized as a serious problem for the establishment of the safety society. Many studies have been done to elucidate the injury generation mechanism of the brain by using the finite element (FE) analyses. In this study, a multi-scale finite element code is newly developed to assess the head injury by employing the stress and strain based criterion. The nonlinear viscoelastic constitutive equation is employed both for the macroscopic and the microscopic scales. Macroscopic head model consists of the skull, cerebral spinal fluid (CSF), facial bone and brain tissue. Microscopic model consists of the blood vessels, blood and brain tissue. When the human head is loaded by the translational acceleration in the traffic accident, the human brain is damaged at the crash side and the counter side, such as the coup and the contre-coup brain injuries. At the macro scale, the compressive hydraulic pressure was concentrated on the coup side, and the expansive hydraulic pressure on the contre-coup side. By employing the boundary velocity, which is derived from the macro FE analysis, the micro FE analysis is carried out. It shows that a very high equivalent stress, obtained by high tensile and shear stresses, occurred in the blood vessel. It was suggested that this multi-scale FE analysis could predict the blood vessel injury by employing the critical injury stress-strain criterion at the macro and micro scale.