A considerable number of pneumatic tyres fail during service as a result of fatigue. Initially, fatigue cracks are formed at points of stress concentration, which may lead to mechanical and thermal failures. The types of fatigue failure include: failure of the tyre carcass, failure of the breaker (including failure in the breaker edge zone), bead failure, and tread separation. To increase the fatigue strength of tyres during service calculation and forecasting of the fatigue strength of tyre parts in the zones of stress concentration are necessary. A tyre mathematical model for calculation of the stress concentration should take into account features of the stress-strain state (SSS) distribution in the concentration zone. The finite element method (FEM) is most suitable for calculating the stress concentration in the rubber-cord parts of the tyre. It makes it possible to describe the complex, multilayer structure of the tyre without any significant simplifications. To assess the fatigue strength of the rubber-cord composite, it is necessary to plot the fatigue curve of the rubber-cord material for the same parameters of the SSS cycle and the same type of SSS as that observed in the zone of failure. The plotting of fatigue curves on the basis of tests of single-layer rubber-cord specimens in the form of rectangular sheets with cord strands arranged at a certain angle to the elongation axis of the specimen is promising. The type of strain state affects the fatigue strength. The static component of the deformation cycle reduces the fatigue strength. For deformation cycles with a static component, characteristic of the rubber matrix material of pneumatic tyres, the maximum value of strain within a cycle can be adopted as the fatigue strength criterion. Increase in the test temperature also lowers the fatigue strength of the rubber-cord material. The proposed procedure for assessing the fatigue life of pneumatic tyres on the basis of calculating SSS concentrations by the finite element method and experimental estimation of the fatigue strength of rubber-cord systems using rubber-cord specimens can be used in pneumatic tyre design practice. For its broad testing, a dataset on the SSS parameters of different types of tyre at points of SSS concentration, obtained by mathematical or experimental methods, is necessary. It is also necessary to continue to obtain characteristics of the fatigue life of rubber-cord systems (Wöhler curves) for different types of SSS and the parameters of the deformation cycle, and it necessary to establish the standard values of the fatigue life limit for different types of rubber. From the results of bench and service tests, standard values of the fatigue strength safety factor for different tyre parts can be determined.