Crystalline sapphire (Al2O3) is a hard and transparent material widely used in industry. When applying IR laser wavelengths, sapphire can be laser-processed inside the bulk (sub-surface) to produce 3D structures, which can find uses, for example, in the production of microfluidic devices. Ul-trashort and tightly focused laser pulses trigger several energy absorption mechanisms inside the bulk. The absorbed energy locally modifies the structure of sapphire. Existing (numerical) models of sap-phire laser processing describe mainly femtosecond pulsed laser-material interaction (most of them only addressing surface processing) and, in addition, these models do not simulate the laser-induced temperatures of the lattice. Therefore, this study is aimed at a 2D-axisymmetric, time dependent, numerical model of the physics in picosecond laser-material interaction with sapphire. The physical phenomena in model include, but are not limited to: multiphoton absorption, tunneling ionization, avalanche ionization, recombination of carriers, diffusion of carriers and heat diffusion. Based on these phenomena, three quantities are calculated, namely: electron density, electron temperature and lattice temperature. The model was implemented in COMSOL Multiphysics®. It was found that, sapphire is modified by the laser radiation only if avalanche ionisation is triggered in the bulk.