Non-Newtonian fluid flow characteristics in inflatable and collapsible elastic tubes are relevant to bio-fluid mechanics and other applications. The radial velocity profiles in an elastic tube during steady laminar flow of a shear thinning aqueous solution of 1.5% carboxy methyl cellulose (CMC) were investigated using ultrasound Doppler velocimetry. The shear ratedependent viscosities obtained using a rheometer were well represented by the Carreau model. Measured storage and loss moduli indicated the CMC solution to be inelastic up to 2% concentration. The velocity profiles were predicted by integrating the theoretical equation derived by equating the shear stress along the tube radius involving pressure drop to that of the Carreau model using its parameters. The agreement between predicted and measured velocity profiles was good. The predicted pressure drop is about the same as the experimental value at lower flow rates. In contrast, the measured pressure drop is lower than that predicted at higher flow rates due to inflation of the tube. Good agreement between estimation (Hagen-Poiseuille's law) and measurement (tube shape image analysis) for the detection of elastic tube expansion while increasing flow rates is found.