Abstarct: One of the major problems of the oil and gas industry is the sand particles found during the extraction procedure. The amount of extracted sand is of high importance since it may lead to many troubles. There are three main problems including pressure drop, tube obstruction and erosion. The erosion is a complex mechanical process in which the material of the pipelines wall surface are removed due to the repetition of the collision of sand particles with the tube wall. Finding the governing parameters on the erosion phenomenon and obtaining a method to model them is necessary. In the present thesis, the effective key factors on the erosion are described and the existing erosion equations have been investigated. In addition, mechanical and experimental models have been used to predict erosion in the pipelines. These models are employed by oil and gas companies to investigate the extent of erosion. The purpose of this research is to numerically investigate the particle motion inside the pipeline elbow and the effect of a change in the velocity, size, and density of the particles, and the kinetic energy of turbulent flow on the erosion rate is also studied. The geometry of the study is a right angled elbow with a 3D steady turbulent flow like almost any other industrial flow. The continuous flow field is obtained by solving the continuity and momentum equations. The particle motion path is achieved by using the one-way coupling Lagrangian tracking model. Finally, a corrosion model is used to investigate the corrosion phenomenon of particles. Another assumptions considered herein is that the sand particles are semi-rounded. The results indicated that the particle size and the particle velocity have the largest effect on erosion rate. As the particle size increased two times, the erosion rate decreases by about 25% and increases about 80% when the particle size decrease 2.5 times. This is caused because the small particles are trapped in the vortices and frequently impact the wall. When the particle velocity is reduced two times, the erosion rate decreases about 80%, and when the particle velocity increased twice, the erosion rate increases 430%.