This Monte Carlo study, utilizing variable sampling approach, is to systematically investigatethe estimation of covariance matrices from incomplete data. The parametersstudied were generalized variance, trace of a matrix, and the largest root. Five factors which related to sampling plan were included: number of variables, average correlationamong variables, sample size, proportion of variable sampling, pattern of design. The sampling plans were organized by balanced incomplete block design (BIBD) and partially balanced incomplete block design (PBIBD). There were 56 conditions studied. The results of estimates were quite biased, especially those of generalized variance. Some negative-definite matrices occured for high correlation matrices, small sample. Among the factors studied, average correlation among variables seems to be the most importantone. There were no consistent pattern for the rest of the factors in terms of accuracy of estimation. Surprisely, the estimation from the large sample size was not substantially better than those from the small sample size.