The stochastic arithmetic is a modelization of the synchronous implementation of the CESTAC method. The behaviour of the Gaussian elimination algorithm performed with the stochastique arithmetic is studied in this paper. It is shown that, using this arithmetic, the algorithm and provided results may be validated. The computation of a maximum of several real values is studied using stochastic arithmetic. It leads to an algorithm in which, when the pivot strategy is applied, stochastic zeroes (unsignificant values) are eliminated from the choice of the pivot automatically.