Construction of computational blood flow models from magnetic resonance (MR) scans of real arteries is a powerful tool for studying arterial hemodynamics. In this report we experimentally determine a lower bound for errors associated with such an approach, and present techniques for minimizing such errors. A known, simple three-dimensional geometry (cylindrical tube) was imaged using a commercial MR scanner, and the resulting images were used to construct finite element flow models. Computed wall-shear stresses were compared to known values and peak errors of 40-60% were found. These errors can be attributed to limited spatial resolution, image segmentation and model construction. A simple smoothing technique markedly reduced these peak errors. We conclude that smoothing is required in the construction of arterial models from in vivo MR images. If used appropriately, such images can be used to construct acceptably accurate computational models of realistic arterial geometries.