A fence construction system in which pickets (52) are attached to rails (50, 51) using fastening means located inside the rails. In one embodiment the pickets are fastened to a rail by a common locking rod. In another embodiment, the pickets (52) are deformed inside the rail (51) by a crimping tool. Equipment that facilitates assembling of the fence may be provided. Top or bottom rails may also have a support structure provided within the rail.