The in-plane and bending stiffnesses of the outer hair cell wall are characteristics crucial to the understanding of force and energy transmission between cochlear elements. A mathematical interpretation is given of the micropipet experiment directed at determining the outer hair cell wall stiffness. On the basis of the microstructural observation of the wall showing that it comprises protein networks with different elastic properties, the model of an orthotropic cylindrical shell is used. The boundary-value problem is analyzed corresponding to the stress–strain state of the wall (shell) caused by the action of the micropipet. The solution is given in terms of Fourier series with respect to the circumferential coordinate. An asymptotic analysis of the solution is developed and an approximate formula for the length of the tongue aspirated within the pipet is derived. This leads to an analytical expression for the stiffness parameter measured in the micropipet experiment in terms of Young’s moduli and Poisson’s ratios of the wall. This expression is an important part of the estimation of the elastic constants of the wall.