The use of mathematical and numerical techniques to elucidate arterial hemodynamics has increased in recent years owing to the prevalence of arterial diseases. Many works have appeared employing three-dimensional models to simulate blood flow in arteries. However, this comes at a huge computational cost and power. In this work, a mathematical model for simulating and predicting blood flow dynamics in an arterial vessel has been developed to meet the teeming need for a computationally-cheap numerical model. The time-dependent one-dimensional hyperbolic system of quasilinear partial differential equations was established from the consideration of physical conservation laws of momentum and mass. This fluid-structure interaction model also incorporates an elastic mural model of the compliant arterial wall material. The combined arterial flow model was solved to simulate flow in the iliac artery using the method of lines. The results revealed that arterial hemodynamics can be adequately captured by a one-dimensional model as proposed. Also, the simulations generated for idealized healthy states could serve as a base model for the numerical simulation of diseased states in the artery.