Road safety analysis is important for vehicles that travel at high speeds. This study proposes a novel viability kernel calculation method for road safety analysis. The viability kernel can be represented by a polyhedron, which is suitable for calculation of the algorithm. This facility solves the problem of analysing the permanent admissible areas of the road with constrains and all possible input of the vehicle. First, the concepts of the viability kernel are described and a simplified vehicle model is developed. Second, the viability kernel is applied to analyse road safety for vehicles on a straight road. Third, the analyses are extended to a straight-corner-straight model, which can be used to simulate general road conditions. The proposed method can predict the largest safety area of the road for vehicles travelling at a high constant speed. In the future, the proposed methods can be applied to calculate the radical safe control for high-speed vehicles in complex road circumstances.