Microtubules (MTs) are the most rigid filaments of eukaryotic cytoskeleton and largely responsible for shape and mechanical rigidity of cells. In view of the fact that microtubules exhibit strong anisotropic elastic properties, an orthotropic elastic shell model for microtubules is developed to study buckling behavior of microtubules. The predicted critical pressure is found to agree well with recent unexplained experimental data on pressure-induced buckling of microtubules which are lower than that predicted by isotropic shell model by four orders of magnitude. General buckling behavior of microtubules under axial compression or radial pressure is studied. The results show that isotropic shell model greatly overestimates the bucking loads of microtubules, except column-like axially compressed buckling of long microtubules (of length-to-diameter ratio larger than, say 150). In particular, the present results also offer a plausible explanation for the length-dependency of flexibility of microtubules reported in the literature.
