The present paper reports the development of Finite Particle Method (FPM) in the framework of a high-speed water jet simulation. The FPM kernel is used to improve the consistency of standard SPH for non-uniform particle distribution. The time integration is performed with a modified Verlet scheme. At the end of each time step, a particle shifting method is applied to mitigate the particle clustering issue by restoring a uniform particle spacing. The influence of particle spacing and maximum CFL number are investigated in the case of a high-speed water jet impinging on a flat plate. The influence of the impinging angle is analyzed for three different angles: 90°, 60° and 30°. The time history of the pressure coefficient is recorded on the flat plate to compare the FPM simulations with available measurements and grid-based CFD simulations. The validation of the results are based on the comparison of the averaged pressure coefficient profile as well as the comparison of the free surface location for the three different impinging angles.