Acoustic Emission (AE) is a phenomenon caused by the emission and propagation of elastic waves generated from micro-cracking. A procedure named “SiGMA” (simplified Green's function for moment tensor analysis) to identify the crack kinematics from AE waveforms has been developed recently. Using this procedure, the crack location, crack orientation and crack type can be determined. Computer software for the SiGMA procedure has been developed and applied in practice. To apply the SiGMA procedure for AE source inversion in a thin plate and other two-dimensional (2D) models, the SiGMA-2D procedure is proposed in this paper. The most distinctive feature of this procedure is projection of 3D moment tensor components onto a plane. For confirmation of SiGMA-2D solutions in practical AE waveforms, the in-plane uniaxial compression tests of plates, which are made by mortar having an internal through-thickness slit, are carried out. The results confirm the applicability of the SiGMA-2D procedure for elucidating the crack mechanisms in 2D models. Further, estimation of crack volume is proposed. For this purpose, the AE sensors are quantitatively calibrated using the Davies-bar technique. A laser opto-interferometer is used to measure the oscillation at the bar end. These results are applied to determination of micro-crack volume.