A universal rail mounting bracket for attachment of a handrail or fence rail to a support structure. An adapter is also disclosed which is matingly engageable with the bracket, the adapter providing a suitable geometric mating surface with a support structure to which the rail will be attached, such as a wall, fence post, or column. By substitution of the adapter portion, the bracket portion can be adapted to virtually any surface and can support the attachment of the rail such that is may extend at any desired angle.