stiff as a board
Also, stiff as a poker. Inflexible, rigidly formal, unbending, as in This cloth is stiff as a board; what happened to it? or There he stood, stiff as a poker, unwilling to give an inch. The board in the first simile for rigidity is a slab of wood; the second, alluding to the iron implement used to push around logs in open fires, dates from the late 1700s.