Although micro-focused Brillouin light scattering (BLS) has been used for more than 20 years, it lacks a complete theoretical description. This complicates the analysis of experimental data and significantly limits the information that can be obtained. To fill this knowledge gap, we have developed a semi-analytical model based on the mesoscopic continuous medium approach. The model consists of the following steps: calculation of the incident electric field and the dynamic susceptibility, calculation of the induced polarization, and calculation of the emitted electric field and its propagation towards the detector. We demonstrate the model on the examples of the measurements of thermal and coherently excited spin waves. However, the used approach is general and can describe any micro-focused Brillouin light scattering experiment. The model can also bring new analytical approaches to mechanobiology experiments or to characterization of acoustic wave-based devices. Published by the American Physical Society 2024