Existing models can hardly provide a reliable guidance in designing intensifier utilizing axial vibration energy of drill strings. The formation process of jet and the pulsation characteristics of flow field had not been reported. Therefore, a new model combined plunger movement and nozzle pressure drop is proposed. The jet formation process, characteristic of water jet distribution, pressurization performance, and impinging pressure under different parameters were studied based on a computational fluid dynamics (CFD) method. The results show that there is a good agreement between the model and the CFD. Increasing the plunger diameter can prolong the holding time of the high-pressure water jet and increase the peak pressure, but it does not affect the pressurization period, which is mainly influenced by the spring. There are three representative stages observed in the forming process of high-pressure water jet, and in stable potential core stage, the inlet pressure does not affect the length of potential core, which is about seven times the nozzle diameter. The impinging pressure decreases with the radial distance, the maximum of which is at the center of the jet. The stand-off distance should be less than 7d, otherwise the impinging pressure will decrease sharply. The research can provide a reference for the optimal design of intensifier and will be beneficial for downhole pressurized jet-assisted drilling techniques.