Discriminant analysis is a supervised learning technique that can be used in order to determine which variables are the best predictors of the classification of objects belonging to a population into predetermined classes. At the same time, discriminant analysis provides a powerful tool that enables researchers to make predictions regarding the classification of new objects into predefined classes. The main goal of discriminant analysis is to determine which of the N descriptive variables have the most discriminatory power, that is, which of them are the most relevant for the classification of objects into classes. In order to classify objects, we need a mathematical model that provides the rules for optimal allocation. This is the classifier. In this paper we will discuss three of the most important models of classification: the Bayesian criterion, the Mahalanobis criterion and the Fisher criterion. In this paper, we will use discriminant analysis to classify the insurance companies that operated on the Romanian market in 2006. We have selected a number of eigth (8) relevant variables: gross written premium (GR_WRI_PRE), net mathematical reserves (NET_M_PES), gross claims paid (GR_CL_PAID), net premium reserves (NET_PRE_RES), net claim reserves (NET_CL_RES), net income (NE—_INCOME), share capital (SHARE_CAP) and gross written premium ceded in Reinsurance (GR_WRI_PRE_CED). Before proceeding to discriminant analysis, we performed cluster analysis on the initial data in order to identify classes (clusters) that emerge from the data.