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This paper presents synthesis of acoustic-emission (AE) wave propagation in multi-layer materials and simulation of AE wave responses at free surface. In particular, the AE source is modelled as an arbitrary-orientation dislocation over an inclined-to- surface fault within one layer or at the layer-to-layer interface, while the materials are assumed as multi-layer media, each of which is homogeneous, isotropic and linearly elastic. With the use of the integral transformation approach, the three-dimensional wave propagation in the materials is solved in transformed or frequency-wavenumber domain. Subsequently, a closed-form solution for wave responses at free surface is found, which can then be converted in time-space domain. Numerical examples are finally provided for illustration. [ABSTRACT FROM AUTHOR]