In this contribution we focus on the computational aspects for practical use of the uncertainty propagation in groundwater flow environment using stochastic finite element method based on generalized polynomial chaos (gPC), where the uncertain part is taking place only in the spatial distribution of the transport properties. In recent years, there has been a growing trend towards real world applications in computational mechanics, thus the reduction techniques have become very desirable. Our focus is on efficient Matlab implementation in terms of computational time and memory consumption without modifying the mathematical background.