a straight face
An emotionless facial expression, especially in a humorous situation that could easily cause one to laugh. It's so hard to keep a straight face on camera when you have hilarious co-stars like I do.
*straight face
Fig. a face free from smiles or laughter. (*Typically: have ~; keep ~.) It's hard to keep a straight face when someone tells a funny joke.
(keep) a straight ˈface
manage not to laugh: When she told me about her accident with the pig, I couldn’t keep a straight face.