Micro-blasting is a general process for surface treatment of engineering components such as gears, dental implants, and screws. These components are put under solid particle impacts. To attain the acceptable final surface, it is important to present an accurate and fast prediction of erosion rate and other surface damage mechanisms of them under various conditions. To reduce the computational costs, this article aims to present a beneficial 3D model using representative volume element (RVE) technique for the simulation of multiple arbitrary angular solid particle erosion (SPE). This technique is used in finite element (FE) method in comparison with smoothed particle hydrodynamics (SPH) to investigate their capability in SPE modeling. Johnson-Cook constitutive equations are performed to describe the erosive behavior of the titanium alloy. To verify the developed approach, SPE experiments were conducted on Ti-6Al-4V under various values of impact angle and particle velocity. Then, the effects of the impact angle on erosion rates are investigated to identify the critical angle in which the erosion rate is maximum. Moreover, an approximate equation is presented for variations of erosion rate. The article focuses on the erosion effect on the surface of the alloy by investigating SPE mechanisms. The results show the RVE approach, as well as the approximate equation, can predict the wear damage in a good agreement with the empirical data. SPH showed more accurate results in higher velocities, while the FE model is more appropriate in the lower ones. According to the results, the impacting angle of 45̊ is critical.