The report is devoted to detection of multivariate abnormal observastions in linear random models. An outlier detection criterion based on residuals from best lineat prediction (best with respect to mean squared error) of the unknown random component is presented and analysed. The relationship between outliers in random and fixed models is investigated. It is shown that the best linear predictor criterion is a sum of two variables. One of the variables in the sum may be use to detect abnormal values of the random component