We present an analysis of how vessel curvature can create distortions in magnetic resonance images of flowing blood. Steady flow in curved vessels produces distortions of the vessel shape and intensity variations in the image due to motion during the interval between phase encoding or slice selection and the echo center. Even with steady flow, vessel curvature produces motion moments higher than velocity (acceleration, etc.), but use of a first order oblique flow compensated phase encoding gradient waveform reduced the distortion in the image. Numerical calculations of image distortions based on simple flow models are in good agreement with experimental results in a phantom.