The Random Neural Network (RNN) has extensively investigated over the past few decades; this research has resulted in a considerable number of theoretical and application papers. Although, great effort has been done to develop a systematic procedure to train the recurrent fashion of the RNN, the choice of the number of neurons remains an open question. To overcome this problem, at least partially, this paper uses multi objective optimisation (MOP) to select the number of neurons. The MOP framework used the mean square error (MSE) and the number of neurons (N) as the objectives to be minimised. The stochastic nondominated algorithm (SNA) to exclude dominated solutions of the Pareto-set has been also introduced. Instead of using only the best solution, candidates to the Pareto-set are excluded by statistical comparison among mean values of the two objectives in all training runs. The SNA allows a statistically correct exclusion of dominated solutions; the best solution can be picked up using classical decision-making procedures. Numerical and real examples illustrate the potentiality of the proposed method in two areas: classification problems and system identification.