We estimate the parameters of an elliptical distribution by means of a multivariate exten- sion of the Method of Simulated Quantiles (MSQ) of Dominicy and Veredas (2010). The multivariate extension entails the challenge of the construction of a function of quantiles that is informative about the … covariation parameters. The interquantile range of a projection of pairwise random variables onto the 45 degree line is very informative about the covariation of the two random variables. MSQ provides the asymptotic theory for the estimators and a Monte Carlo study reveals good nite sample properties of the estimators. An empirical application to 22 worldwide nancial market returns illustrates the usefulness of the method.