A computational mathematical model simulating thermal and electrical behaviour of thermoelectric generators has been developed, based on a model which solves non-linear systems formed by thermoelectric and heat transfer equations. The model enables us to calculate the values of temperatures, efficiency, power, electrical tension and current which would be generated in the system, given: the thermoelectric parameters dependent on the temperature boundary conditions, room temperature and flux of residual heat. Finite differences method is used in order to solve the system and also semi empirical expressions for convection coefficients. Test bench has been made for validated mathematical model, with experimental data of thermoelectric generation. Thermal resistance and thermal capacity of the elements of the test bench have been calculated to improve accuracy in the simulated values with the model. The purpose of this paper is to obtain a design tool that allows us to solve the equation system of thermoelectric generation with no need to make previous prototypes, with the benefit of being money saving and more possibilities to simulated cases. These results will correct the error taking the thermoelectric parameters dependent on the temperature and will correct some errors existing in a related research as well as provide some theoretical basis for the optimum design of a real thermoelectric generator.