Monte Carlo simulation compared chi-square statistics, parameter estimates, and root mean square error of approximation values using normal and elliptical estimation methods. Three research conditions were imposed on the simulated data: sample size, population contamination percent, and kurtosis. A Bentler-Weeks structural model established the relationship between the sample variance-covariance matrix and the specified population model. The elliptical generalized least squares estimation method provided the better chi-square results in the presence of kurtosis. The parameter estimates were similar across research conditions for both the normal and elliptical estimation methods. The root mean square error of approximation values was robust in the presence of kurtosis for the elliptical estimation methods. The root mean square error of approximation is, therefore, the preferred inferential approach to assessing model fit in the presence of kurtosis because of known distributional properties and determination of confidence intervals for hypothesis testing. An appendix contains the EQS 5.7 computer program for the analysis. (Contains 3 figures, 18 tables, and 40 references.) (Author/SLD)