Membrane budding and fission are the key stages of ubiquitous processes of formation of intracellular transport vesicles. We present a theoretical consideration of one of the most important types of fission machinery, which is mediated by GTPase dynamin and controlled by lipid composition of the membrane. We suggest a mechanism for collapse of a membrane neck driven by interplay between the dynamin collar and the bending elastic energy of the neck membrane. The collar plays a role of a rigid external skeleton, which imposes mechanical constraints on the neck. We show that in certain conditions the membrane of the neck loses its stability and collapses. Collapse can result from: (i) shifting of the spontaneous curvature of the neck membrane towards negative values, (ii) stretching of the dynamin collar, (iii) tightening of the dynamin collar. The three factors can act separately or concertedly. The suggested model accounts for the major experimental knowledge on membrane fission mediated by dynamin. It includes the elements of all previous models of dynamin action based on different sets of experimental results [Sever et al., Traffic 2000; 1: 385-392]. It reconciles, at least partially, the apparent contradictions between the existing alternative views on biomembrane fission machinery.