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Stock market indices' rate of return distributions is a recurrent theme in financial literature, especially because some models require the normality assumption as premise. Following the works of Ingersoll Jr. (1987) and Hamada & Valdez (2004), the empirical distribution of the Ibovespa and S&P500 rates of returns from 1986 to 2006 was analyzed. As reported by some others authors, for both indices, the results evidenced that the normality assumption can be highly questionable, because other theoretical distributions from the elliptical family fitted the data better. The rates of return for the Brazilian and American indices showed leptokurtosis, and, in the Brazilian case, asymmetric shape, so that only distributions that deal with these parameters in a less restrictive way, as the Logistic or Log-logistic distributions, can show a better fit to the observed data. [ABSTRACT FROM AUTHOR]