How can you claim a deceased parents bank account.?

What you will want to do is contact the bank and have them pull his Beneficiary information. When you open an account it is customary to fill out a Beneficiary card or form. If your name is on the card and you provide a copy of your father's death certificate you should receive the money that he wanted you to have. You will also have to prove who you are via a SS card and normally two forms of identification from the Federal and/or state government. Another thing to keep in mind is that years ago he may have changed the Beneficiary to be someone else other than you. If there is no designated Beneficiary then he is said to be intestate and a court will have to decide by using will information, living trust data and the laws of succession which could take years in probate court.

You'd need to go to court and have yourself named as the administrator of his estate. You'll have to show due diligence in taking care of any of his legitimate debts before you can distribute the proceeds of his accounts.

Is your mom still living? If so, this should be her task, not yours. Some or all of his estate might actually be hers now.