Once formed, fusion pores rapidly enlarge to semi-stable conductance values. The membranes lining the fusion pore are continuous bilayer structures, so variations of conductance in time reflect bending and stretching of membranes. We therefore modeled the evolution of fusion pores using the theory of the mechanics of deforming homogeneous membranes. We calculated the changes in length and width of theoretical fusion pores according to standard dynamical equations of motion. Theoretical fusion pores quickly achieve semi-stable dimensions, which correspond to energy minima located in a canyon between energy barriers. The height of the barrier preventing pore expansion diminishes along the dimensions of length and width. The bottom of the canyon slopes gently downward along increasing length. As a consequence, theoretical fusion pores slowly lengthen and widen as the dimensions migrate along the bottom of the canyon, until the barrier vanishes and the pore rapidly enlarges. The dynamics of growth is sensitive to tension, spontaneous curvature, bending elasticity, and mobilities. This sensitivity can account for the quantitative differences in pore evolution observed in two experimental systems: HA-expressing cells fusing to planar bilayer membranes and beige mouse mast cell degranulation. We conclude that the mechanics of membranes could cause the phenomenon of stagewise growth of fusion pores.