This work deals with the numerical application of a recently developed method, High Dimensional Model Representation (HDMR), to multivariate Poisson Equation. HDMR is constructed to express a given multivariate function as a sum of components whose multivariance ascends starting from constancy, continuing with univariate, bivariate terms and so on. These components satisfy certain orthogonality conditions. If the HDMR of the unknowns is inserted into the Poisson equation and the orthogonality conditions are used then integro-differential equations are obtained. The truncation by omitting higher than certain multivariance terms simplifies the interaction between equations. Here, only constant and univariate terms are considered as an approximation. (c) 2004 WILEY-VCH Verhag GmbH & Co. KGaA, Weinheim.