Lutetium-177, one of the current global research hotspots for medical isotopes, can be produced by reactor irradiation of lutetium-176, which can be produced and processed with the assistance of the electron beam physical vapor deposition (EB-PVD). The metal evaporation process is an important part of EB-PVD, which aims to convert solid metal into metal atomic vapor. The distribution of each macroscopic characteristic quantity, such as thermal population distribution, density distribution, velocity distribution, and temperature distribution of metal atomic vapor, will directly affect the utilization of metal vapor atoms, the subsequent deposition process, and coating process. In this paper, two-dimensional model and three-dimensional model of the metal evaporation process are established based on the direct simulation Monte Carlo method, and atomic metastable state is introduced into the collision assumption. The macroscopic characteristic quantities, such as the number density of metal atomic vapor, the motion velocity and the discrete degree of the total motion velocity in the evaporation process with or without considering the lutetium atomic metastable state, are analyzed and compared. The spatial distribution characteristics of each energy level of metal atomic vapor are observed, and the variation characteristics of the macroscopic characteristic quantities in the center with the slit opening size and the evaporation source surface temperature are discussed. The study results show that the number density of metal vapor passing through the beam flow device decreases, the average velocity in the x-direction and z-direction and the discrete degree of the total motion velocity increase, with the atomic metastable state taken into consideration. The beam flow device intensifies the transformation of the atomic energy level of the metal vapor and changes the physical parameters of the metal atomic vapor. At the same time, the slit opening size and the evaporation source surface temperature trigger off the change of the macroscopic characteristic quantity distribution of the metal vapor, including the degree of anomalous protrusion of each macroscopic characteristic quantity above the slit. The results of the three-dimensional simulation based on the two-dimensional model are consistent with the changes in the order of magnitude of data distribution and spatial distribution pattern, which can serve as a reference and guidance for the experimental study of the electron beam metal evaporation process.