Both are used. I prefer "is".
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Tomorrow is/will be my mom's birthday.
Are 'is and will be' both correct in the above sentence?
With that construction, I prefer "is". It is tomorrow's date that is important and that date is her birthday every year. I probably wouldn't use that construction at all though. I would say "It's my mum's birthday tomorrow".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.