To diagnose mechanical faults of rotor-bearing-casing system by analyzing its casing vibration signal, this paper proposes a training procedure of a fault classifier based on variational mode decomposition (VMD), local linear embedding (LLE), and support vector machine (SVM). VMD is used first to decompose the casing signal into several modes, which are subsignals usually modulated by fault frequencies. Vibrational features are extracted from both VMD subsignals and the original one. LLE is employed here to reduce the dimensionality of these extracted features and make the samples more separable. Then low-dimensional data sets are used to train the multiclass SVM whose accuracy is tested by classifying the test samples. When the parameters of LLE and SVM are well optimized, this proposed method performs well on experimental data, showing its capacity of diagnosing casing vibration faults.