Shall is more formal, should is more common.

Thank you:)

Knowlton is correct, but I think it is worth mentioning that the two words also have slightly different meanings. 'Shall' is like saying 'will' e.g I shall/will go for a walk. So describing your intention to do something. Should describes something you're supposed to do or need to do, if that makes sense. E.g I should study for my test. The formal word for it would be 'ought' but it's not commonly used in everyday spoken English. I'm not sure if that was a clear explanation...but I hope it helps :)