Summary: The paper considers simultaneous estimation of finite population variances from several strata in the presence of auxiliary information. A general hierarchical Bayes (HB) procedure is introduced for such estimation. The HB estimators are shown to perform better than the usual sample variances by means of some simulated data. Also, in some special cases, the HB estimators are shown to be “asymptotically optimal” in contrast to the sample variances which are asymptotically non-optimal.