Radiological reporting generates a large amount of free-text clinical narratives, a potentially valuable source ofinformation for improving clinical care and supporting research. The use of automatic techniques to analyzesuch reports is necessary to make their content effectively available to radiologists in an aggregated form. In thispaper we focus on the classification of chest computed tomography reports according to a classification schemaproposed for this task by radiologists of the Italian hospital ASST Spedali Civili di Brescia. The proposed system isbuilt exploiting a training data set containing reports annotated by radiologists. Each report is classified accordingto the schema developed by radiologists and textual evidences are marked in the report. The annotationsare then used to train different machine learning based classifiers. We present in this paper a method based on acascade of classifiers which make use of a set of syntactic and semantic features. The resulting system is a novelhierarchical classification system for the given task, that we have experimentally evaluated.