This article discusses various procedures for variance estimation, under the Midzuno-Sen sampling scheme, of the ratio estimator of a finite population total when auxiliary information on two variables is available and suggests some variance estimators. A small scale Monte Carlo simulation is carried out to investigate empirical performance of the suggested estimators. The estimator vopt performs extremely well for the populations having high coefficients of variation of two auxiliary variables and very high coefficients of correlation of the auxiliary variables with the study variables. Otherwise, the estimator v12 and v13 suggested by Chaudhuri [1], perform very well.