Membrane nanotubes play important functional roles in numerous cell activities such as cellular transport and communication. By exerting an external pulling force over a finite region in a membrane patch, here we investigate the size dependence of the membrane nanotube formation under the continuum and atomistic modeling frameworks. It is shown that the membrane undergoes a discontinuous shape transition as the size of the pulling region and the membrane tension increase. A formula characterizing the nonlinear relationship between the maximum static pulling force and pulling size is identified. During the membrane extraction, lipids in the upper and lower leaflets exhibit different behaviors of structural rearrangements. Moreover, our computational simulations indicate that the steady state pulling force increases linearly with the pulling velocity as well as the size of the pulling region.