Is it ever normal for a 7-8 year old to hit & punch self when upset or frustrated?

FRUSTRATION: Kids this age are usually well behaved but occasionally due to extreme frustruation they hit themselves. If the behavior is habitual they should be evaluated for depression.

No: It is not normal. Needs to be evaluated for behavior problem and anger control. Attention and proper counseling now will help a lot later on. Please seek help with counseling and/or pediatrician.

Need alternative: It actually is not all that uncommon for kids this age to self-punish when upset. First, acknowledge with the child it is ok to feel upset/frustrated. We all have these emotions because we are human. But have it worked out ahead of time when they are feeling that way, what are appropriate ways to deal with those feelings. Some kids draw, punch a punching bag, tear up old newspapers or rags, etc.