Should of, Would of, Could of — is it of or have?

The use of should of, would of, could of (and even will of) in written English seems to be on the increase.

These errors appear to stem from the fact that the contractions would’ve, should’ve and could’ve sound like would of, should of and could of. The use of the word of in these cases is incorrect according to current English usage.

A quick Google search will show that the use of these incorrect phrases is quite common. Some linguists speculate that these uses will in time become so common that they will be officially accepted as Standard English. However, the vast majority of people currently consider these phrases to be grave errors.

When writing, we recommend taking care to use the correct form.

Source: Oxford English Dictionary