Highly anisotropic microtubules (MTs) immersed in cytosol are a central part of the cytoskeleton in eukaryotic cells. The dynamic behaviors of an MT-cytosol system are of major interest in biomechanics community. Such a solid-fluid system is characterized by a Reynolds number of the order 10(-3) and a slip ionic layer formed at the MT-cytosol interface. In view of these unique features, an orthotropic shell-Stokes flow model with a slip boundary condition has been developed to explore the distinctive dynamic behaviors of MTs in cytosol. Three types of motions have been identified, i.e., (a) undamped and damped torsional vibration, (b) damped longitudinal vibration, and (c) overdamped bending and radial motions. The exponentially decaying bending motion given by the present model is found to be in qualitative agreement with the existing experimental observation [Felgner et al., 1996. Flexural rigidity of microtubules measured with the use of optical tweezers, Journal of Cell Science 109, 509-516 ].