In the process of oil and natural gas production, solid particle erosion is an important reason affecting the safe operation of oil and gas multiphase pumps. To reduce equipment failure rates, it is urgent to predict positions that are vulnerable to erosion damage. However, the erosion regularities of oil and gas multiphase pumps have rarely been studied in the past. In this paper, the Euler-Lagrange method is used to analyze the gas-liquid-solid flow phenomena in oil and gas multiphase pumps under different operating conditions, combined with the Oka model for erosion prediction. The validity of the erosion prediction method is verified using numerical simulation results of erosion at 90° elbows. To explore the erosion mechanism between fluid and entrained particle flow behavior, the relationship between particle parameters and erosion position and regularities is emphatically studied. The research results indicate that in a certain range, the maximum erosion rate of the oil and gas multiphase pump decreases with the increase of particle density, but increases linearly with the fluid velocity and is also affected by gas volume fraction and other particle parameters. In addition, the erosion usually occurs on the inlet, outlet wall, and the leading edge of the pump chamber, due to the different particle parameters, the erosion range will be slightly different. According to the particle trajectory, it is found that the leading edge of the pump chamber is the most erodible region due to the high frequency and intensity of particle impact. These results provide a reference for optimizing the structural design of the oil and gas multiphase pumps and help to predict their performance against wear.