Ultrashort pulse laser processing is highly valued due to its enormous potential for high micromachining quality while it comprises complicated physical mechanisms especially when the pulse width falls in the regime about 10 ps. This study presents a complete mathematical modeling on multi-phase phenomena in ultrashort pulse laser processing, such as melting, vaporization, and solidification. The volume of fluid (VOF) technique is used to capture the interface during phase transition. Based on this hybrid model, the transport of energy and mass are investigated to study the influence of laser parameters on the formation of laser ablation hole. This work develops the incompressible multiphase laser ablation solver based on PIMPLE algorithm. The calculation results are validated by different references under different laser processing parameters which emphasize the importance of mechanism on thermal ablation and hydrodynamics in picosecond laser processing. More calculation results about the trends in hole depth over pulse laser width, laser fluence, and the number of pulses show the intricate influence of laser parameters.