Hardware-implemented machine learning algorithms are finding their way in various domains, including safety-critical applications. This has demanded these algorithms to perform correctly even in harsh environmental conditions, such as in avionics altitudes. Support Vector Machine (SVM) is an important Machine Learning that has been target of hardware implementation in recent years. This is the first work to asses both Binary and Multiclass SVMs under thermal neutron radiation, a type of particle noticeably present in high altitudes. A fault injection campaign along with a radiation test with the D50 thermal neutron source, at the Intitut Laue-Languevin, has been performed. The results show a high intrinsic fault tolerance for both varieties of the SVM algorithm, especially for the Multiclass SVM.