straight faced TFD straight′-faced′ (-fāst′) adj. straight′-faced′ly (-fāst′lē, -fā′sĭd-lē) adv.
A face that betrays no sign of emotion.
As in:
He was a very straight-faced prof, but he has a tremendous sense of humor.
She was watching me totally straight-faced and it took a couple of seconds before it dawned on me that I'd just been had.
And here is an article on some famous straight-faced comedians: article