Various compression algorithms for multi-channel electroencephalograms (EEG) are proposed and compared. The multi-channel EEG is represented as a three-way tensor (or 3D volume) to exploit both spatial and temporal correlations efficiently. A general two-stage coding framework is developed for multi-channel EEG compression. In the first stage, we consider (i) wavelet-based volumetric coding; (ii) energy-based lossless compression of wavelet subbands; (iii) tensor decomposition based coding. In the second stage, the residual is quantized and coded. Through such two-stage approach, one can control the maximum error (worst-case distortion). Numerical results for a standard EEG data set show that tensor-based coding achieves lower worst-case error and comparable average error than the wavelet- and energy-based schemes.