A magnetic resonance imaging (MRI) tubular rheometer for polymer melt systems is described. This technique allows the viscosity to be determined over a range of shear rates. It relies upon obtaining steady-state velocity profiles in tubular pipes using MRI and simultaneously measuring the pressure drop. In these experiments, the shear viscosity of a low-density polyethylene (LDPE) melt was measured at shear rates between 1.8 and 12.1 s(-1) and was found to be approximately 117.7 Pa.s. The viscosity was also determined using a parallel plate rheometer in which it was found to vary slightly with shear rate, ranging from 113.9 to 107.2 Pa.s, comparing favorably with the MRI determined values. MRI is noninvasive and nondestructive and can be applied to opaque systems; hence, it has the potential to be used for in-process monitoring.