Limitations in clinical cardiovascular research have driven the development of advanced simulations for patient-specific insights into arterial elasticity. However, uncertainties in model inputs, data resolution, and parameter estimation can compromise accuracy. Our research aimed to provide reliable estimates of the arterial wall elasticity non-invasively, where direct clinical measurement is difficult. By integrating patient-specific imaging with a simplified flow simulation model and uncertainty quantification, we sought to improve the reliability of these predictions as compared to the state-of-the-art. In a proof-of-concept study, we developed a simple area-averaged model of arterial hemodynamics, using Magnetic Resonance Angiogram (MRA)-derived geometries and input parameters based on the age, cuff blood pressure, and phase-contrast MRI data in five human subjects. This resulted in an in-silico model estimating the pressure and flow variations across the arterial-branches. Statistical uncertainties in the hemodynamic parameter predictions were quantified using non-intrusive Polynomial Chaos. Additionally, we developed a model to estimate the arterial elasticity by interlacing the results from fluid-structure interaction simulation for arterial hemodynamics with patient-specific clinical data. We found that the arterial elasticity values derived from our model, when used to predict the flowrates, closely matched the flow characteristics obtained from the patient-specific 4D flow MRI. The findings also showed zero or minimal positive/negative bias in our simulations, with no noticeable systematic error in predicting arterial elasticity values. Our results evidenced that accurate prediction of arterial wall elasticity is possible through use of an efficient simulation technique supplemented with clinically attainable imaging data. This has potential to predict cardiovascular-risk and guide individual patient management.