The aim of the paper is to present the results of computer experiments that allowed us to investigate some of the properties of LePage series representations of -stable random variables and to check their usefulness to computer simulation of Lvy motion. We base our study on the explicitly obtained formula for the expectation  , where  , with τ_j's denoting the arrival times of a Poisson process and   appropriately chosen discrete random variables, and where X denotes an a.s. limit of the sequence X_n. We conclude that as far as computer simulations are concerned the sums X_n are not the most suitable means of approximation of X.