The bivariate Weibull distribution is very important in both reliability and survival analysis. The dependence for these kind of problems has been gaining great importance in recent years. In the literature, there are algorithms to generate univariate Weibull distributions and bivariate Weibull distributions with independent marginal distributions. In this paper, we present an algorithm to generate dependent bivariateWeibull failure times using a copula representation for the bivariate Weibull reliability function. Such representation is obtained using archimedean copula models. In particular, we used the Gumbel’s family. An application of the copula algorithm was done and the results were successfully validated.