An encoding method and apparatus and a decoding method and apparatus are provided. The decoding method includes extracting a compatible down-mix signal optimized for a first multi-channel decoder from the input bitstream, converting the compatible down-mix signal to be optimized for a second multi-channel signal by performing a compatibility processing operation on the compatible down-mix signal, and generating a three-dimensional (3D) down-mix signal by performing a 3D rendering operation on the converted down-mix signal. Accordingly, it is possible to efficiently encode multi-channel signals with 3D effects and to adaptively restore and reproduce audio signals with optimum sound quality according to the characteristics of an audio reproduction environment.