The development of advanced carbonaceous materials (ACMs) from biopitches is important to increase the revenue of the charcoal making industry and to stimulate the use of biomass, thereby attending to the appeals for environmental preservation. A pioneer study on the rheological behavior of eucalyptus tar pitches was carried out in this work. This behavior plays an important part in obtaining ACMs from pitch, particularly in the spinning step of carbon fiber production. Our results showed that biopitches have a strong dependence on the viscosity and temperature/softening point ratio. An Arrhenius-type law gave the activation energies for viscous flow. Different from conventional polymers, this energy was higher for more polymerized pitches because of their higher molecular stiffness. The results obtained by the Williams-Landel-Ferry equation showed that the viscosity can be associated with the free volume. Lower viscosities correspond to larger free volume. The plot of the apparent viscosity versus the shear time at constant temperature and shear rate showed that the pitches have a purely viscous flow. Experiments that changed the shear rate showed that biopitches behave as Newtonian fluids. Purely viscous and Newtonian behaviors are desirable for more stable spinning.