Abstract: This paper discusses the jackknife estimators of functions of means in two-stag and three-stage simple random sampling multiyariate populations of finite size, which remove the bias of O(m^-1)（m is the stage-one sample size）. It also gives the estimators of mean sqare errors of the jackknif e estimators. Jones’ （1974） stratified sampling case is a special case of two-stage simple random sampling. Finally it gives two numberio examples of ratio estimators about two-stage and three-stage simple random sampling.