In many regions, the percentage of cardiovascular diseases (CVDs) cases is beyond the alarming level. Most of the CVDs are due to arterial accumulations (atherosclerosis) which is a progressive stiffening of the artery. Although a huge experimental, analytical, and numerical work is dedicated to understand the accumulation phenomenon and its effects on the arterial wall, there is plenty of room available to estimate the deformation behavior of flexible arteries in the presence of accumulation. Present study is dedicated to the numerical modeling of arterial pressure variation due to accumulation and its effects on the structure integrity of arteries. The objective of this study is to predict the response of partially blocked artery due to pulsating blood flow. The Fluid Structure Interaction (FSI) is incorporated in the developed model as it plays a major role in governing the deformation of arteries. Due to highly elastic nature of arteries, two- and three-dimensional hyper-elastic material model is developed via ANSYS Workbench software to define deformation behavior of arteries while blood is assumed as non-Newtonian fluid. Pulsating blood flow condition is applied through piece wise periodic function. Finite element simulations are performed for different geometrical and loading parameters such as thickness of arterial wall, geometry of accumulation to simulate different levels of atherosclerosis and blood pressure. Obtained results from numerical simulations, distribution of wall shear stresses, pressure variation, and equivalent stresses in the artery are investigated. Present study could be utilized to understand atherosclerosis and its effects on the deformation behavior of arteries.