Risk classification is a process of grouping together individuals with similar risk levels into categories that insurance companies use in order to decide how premium rates should differ in each category. This process is conditioned on the information available about the insured and the contract, which is stored in many variables.  Because of the large number of variables and the fact that many interactions exist between them, multivariate analysis techniques such as Principal Component Analysys (to reduce the dimensionality of data) and Cluster Analysis (to group individuals with similar characteristics), are applied for this purpose. Here we recommend the application of both methods to obtain better results.  Insurance data usually contains information regarding unexpected extreme losses (catastrophes), modeled with heavy tailed distributions, which may be considered as outliers. Therefore, robust methods for both multivariate techniques are applied by using an algorithm that implies the use of several robust estimators existing nowadays. We compare our results with those obtained from a classical approach.