Motivated by a problem in archaeological data analysis, we examine through simulation the effect of linear truncation on density estimation in the bivariate normal distribution. It is shown that the estimation procedure performs poorly when the truncation line is parallel to the minor axis of the elliptical contours of the distribution. The estimation also worsens with increasing correlation and increasing disparity in the values of the variances in the distribution. Reconstruction of the bivariate normal distribution is best achieved when truncation is parallel to the major axis and there is only about 10% of the data that is missing.