stiff as a board - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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.