We studied the morphological change in bilayer vesicles induced by mechanical forces using a Brownian dynamics simulation. When bilayer membranes in two vesicles or the same vesicle are pushed from both sides by two nanoparticles, they fuse into a spherical or toroidal vesicle, respectively. Under large forces, the fusion occurs directly after the contact of the distal (trans) monolayers. Stochastically, a fusion intermediate, a disk-shaped bilayer consisting of both inner monolayers is formed under weaker forces. In this intermediate, the fusion pore that connects the insides of the vesicles is formed at the edge of the bilayer disk. These fusion processes are different from those of spontaneous fusion. The toroidal vesicle spontaneously changes back into a spherical shape, because the vesicle is small. The hole of the toroid disappears through a cylindrical stalk.