Recently, statistical researchers have shown increased interest in Gaussian process modeling with mono- tonicity constraints (see [2], [4] and [5]). In computer experiments, the true function (scalar output) may be known to be monotone with respect to some or all input variables. We propose a new methodology based on the Bayesian Gaussian process metamodeling to sample from posterior distribution including monotonicity information in the monovariate case. Let y = f (x) be a monotonic increasing function where the input x is assumed to be scalar and in the domain [0, 1]. We consider a set of computer experiments {(xi , yi ) | i = 1, * * * , n} of size n and assume that yi = f (xi ), 1 ≤ i ≤ n. (1) Also suppose that M is the space of increasing functions and (Yx )x∈[0,1] is a zero-mean Gaussian process (GP) with kernel k(x, xt) given by a priori knowledge about the relationship between the input x and the output y. The following experimental results (see figures below) are obtained with the classical Gaussian kernel. We are interested in the simulation of the conditional (or posterior) distribution of the GP Y given data and monotonicity information...