The focus of this Master’s thesis is the analysis of multi-mode VCSEL and their dynamics. The study proposes a particular emphasis on the contribution that the optical external feedback exerts on the performances of the laser. VCSEL is the acronym for Vertical Cavity Surface Emitting Laser, they are laser diodes that can be pumped directly by an electrical current and have small dimensions (hundreds of micron). In the first part of the thesis, the behaviour of a single-mode and a multi-mode VCSEL are numerically simulated. In order to do that, the evolution of some quantities for different current injected are simulated, such as the carrier density distribution and the output power.