Revealing vibration characteristics of sub-cellular structural components such 
as membranes and microtubules has a principal role in obtaining a deeper 
understanding of their biological functions. Nevertheless, limitations and 
challenges in biological experiments at this scale necessitates the use of 
mathematical and computational models as an alternative solution. As one of the 
three major cytoskeletal filaments, microtubules are highly anisotropic 
structures built from tubulin heterodimers. They are hollow cylindrical shells 
with a ∼ 25 nm outer diameter and are tens of microns long. In this study, a 
mechanical model including the effects of the viscous cytosol and surrounding 
filaments is developed for predicting the coupled oscillations of a single 
microtubule immersed in cytoplasm. The first-order shear deformation shell 
theory for orthotropic materials is used to model the microtubule, whereas the 
motion of the cytosol is analyzed by considering the Stokes flow. The viscous 
cytosol and the microtubule are coupled through the continuity condition across 
the microtubule-cytosol interface. The stress and velocity fields in the cytosol 
induced by vibrating microtubule are analytically determined. Finally, the 
influences of the dynamic viscosity of the cytosol, filament network elasticity, 
microtubule shear modulus, and circumferential wave-number on longitudinal, 
radial, and torsional modes of microtubule vibration are elucidated.