We study an estimation procedure for maximum likelihood estimation in covariance structure analysis with truncated data, and obtain the statistical properties of the estimator as well as a test of the model structure. Truncated data with and without knowledge about the number of unmeasured observations are both considered. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, which requires only first derivatives, is proposed to obtain the maximum likelihood estimates. We illustrate the statistics and parameter estimates by a fictitious example. The maximum likelihood method is compared to an alternative two-stage method.