Simultaneous recordings with multi-channel electrodes are widely used for studying how multiple neurons are recruited for information processing. The recorded signals contain the spike events of a number of adjacent or distant neurons and must be sorted correctly into spike trains of individual neurons. Several mathematical methods have been proposed for spike sorting but the process is difficult in practice, as extracellularly recorded signals are corrupted by biological noise. Moreover, spike sorting is often time-consuming, as it usually requires corrections by human operators. Methods are needed to obtain reliable spike clusters without heavy manual operation. Here, we introduce several methods of spike sorting and compare the accuracy and robustness of their performance by using publicized data of simultaneous extracellular and intracellular recordings of neuronal activity. The best and excellent performance was obtained when a newly proposed filter for spike detection was combined with the wavelet transform and variational Bayes for a finite mixture of Student's t-distributions, namely, robust variational Bayes. Wavelet transform extracts features that are characteristic of the detected spike waveforms and the robust variational Bayes categorizes the extracted features into clusters corresponding to spikes of the individual neurons. The use of Student's t-distributions makes this categorization robust against noisy data points. Some other new methods also exhibited reasonably good performance. We implemented all of the proposed methods in a C++ code named 'EToS' (Efficient Technology of Spike sorting), which is freely available on the Internet.