In this article, a convergence criterion for the Monte Carlo estimates, which can be used as a stopping rule for the Monte Carlo experiments, will be proposed. The proposed criterion seeks a convergence band of a given width and length such that the probability of the Monte Carlo sample means to fall outside of this band is practically null. Although it has some sort of self defined confidence, equivalent values for the parameters of proposed criterion can be determined through a pilot experiment so as to have a predefined confidence level in the usual statistical sense. Since it does not require sequential computation of the Monte Carlo sample variance, it is computationally more efficient than the usual stopping rule. (C) 2006 Elsevier B.V. All rights reserved.