Micro-injection moulding is a relatively new process, and as such it has not been deeply investigated until now. The pecularities related to the three dimensional aspect of the cavity and the very small length and time scales at stake make it a very specific technology compared to conventional injection moulding. The aim of this thesis is to pave the way for micro-injection moulding modelling with a special emphasis on micro-cavity filling. The different steps adopted in this work are the following ones: first an extensive review of the process is proposed, followed by a reflection on micro-cavity filling and polymer behaviour which ends up with the choice of the Giesekus model as an adapted visco-elastic model for some polymers used in this process. A chapter dedicated to polymer characterization conducted on PC Lexan HF11110R, a micro-injection suited amorphous material, shows that the Newtonian viscosity is very low.In this case, the model acceptability on the mathematical and thermodynamical viewpoints is not guaranteed. This acceptability is the object of a chapter which provides an analysis for the Giesekus model completed with the PC Lexan material parameters. A further mathematical consequence of a vanishing Newtonian viscosity is that the number of inlet boundary conditions to be prescribed for the extra-stress tensor is reduced to 4 instead of 6 in case of a non-vanishing Newtonian viscosity. A specific numerical scheme to tackle this problem is proposed along with a theta-splitting based method which allows us to separate the viscous and visco-elastic effects in the governing equations and to treat subsequently a modified Stokes sub-problem and a transport sub-problem. Finally, a micro-mixer design and prototyping is presented as an application of this promising process. ...