Can an Israeli bank go after me as guarantor without first suing the borrower?

It depends on the type of guarantee you signed. If you are an *arev kablan* (undertaking guarantor) or *arev v'meshalem* (joint and several guarantor), the bank can pursue you directly and simultaneously with the borrower, without needing to exhaust action against the primary debtor first. Banks in Israel almost always request one of these two types for mortgage and business loan guarantees precisely because it gives them maximum collection flexibility. Only a simple guarantor (*arev pashut*) has the right to require the creditor to pursue the debtor first.