We conducted a simulation study to compare two semi-parametric approaches for the estimation of covariate effects from multivariate failure time data. The first approach was developed by Wei, Lin and Weissfeld (WLW) and the second by Liang, Self and Chang (LSC). Based on the simulation results we recommend Wei, Lin and Weissfeld's method for the situations with identical covariates and high correlations between the failure times. When the covariates are independent, LSC produces smaller mean squared errors than WLW, although at the expense of larger bias. We also compared four computer programs for implementing Wei, Lin and Weissfeld's approach: a FORTRAN program, MULCOX2; a SAS macro; the coxph function in S-plus, and a specialized software package for complex survey data (SUDAAN). Our comparison indicates that for large data sets, the speeds of the SAS macro and coxph are comparable, while MULCOX2- and SUDAAN took longer to run. However, MULCOX2 and coxph function in S-plus have the advantage of allowing time-dependent covariates, and SUDAAN has the advantage of handling complex survey data.