Viability theory proposes geometric metaphors in addition to classical ordinary differential equation analysis. In this paper, advantages of applying viability theory to road safety domain are presented. The exact issue is to determine if, from an initial state of a vehicle/road/driver system, a soft controls strategy is compatible with a safe driving sequence. The case of a car negotiating a curve is considered. The application of the viability theory to this issue offers the advantage to avoid classical full computing of the system. Instead of that, it consists on verifying that the states and the controls belong to a subset called the viability kernel. The construction and the use of the viability kernel for a vehicle system dynamic is proposed by using support vector machines algorithm. Then, the applicability of this theory is demonstrated through experimental tests. This innovative application of the viability theory to vehicle dynamics with road safety concerns could benefit to robust embedded warning systems.