Experimental characterization of the in-plane stress tensor is a basic requirement for the development of GaN strain engineering. In this work, a theoretical model of stress characterization for GaN using polarized micro-Raman spectroscopy was developed based on elasticity theory and lattice dynamics. Compared with other works, the presented model can give the quantitative relationship between all components of the in-plane stress tensor and the measured Raman shift. The model was verified by a calibration experiment under step-by-step uniaxial compression. By combining the stress characterization model with the expanding cavity model, the in-plane residual stress component field around Berkovich indentation on the (0001) plane GaN was achieved. The experimental results show that the distributions of the stress components, which significantly differed from the distribution of the Raman shift, were closely related to the GaN crystal structure and exhibited a gradient along each crystal direction.