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Archimedean copulas are one of the most known classes of copulas. They allow modeling the dependencies between variables with small number of parameters. This paper presents a method designated to generate multivariate samples of the same distribution like primary sample with Archimedean copulas. Such generator may be used in Monte Carlo investigations to create multivariate samples. Apart from theoretical considerations there are presented the examples of application of the method. All the calculations were carried out with R 2.15.0 packages.