Without the aid of an external program I dont believe there is a way to create a batch of incidents.

Not all at once, but a quick incident could accomplish that with just having to set a contact after the fact.

You could also do a task that would basically create a copy of an incident and then change you'd just have to change the contact there as well.  If you need help with either of those let us know.

You could use an Automation Rule for this purpose.
An Automation Rule allows you to create multiple tickets in the same time, while you can inherit any value from a "mother" ticket.

Using all of the same values of the "mother" ticket is rather simple, the only thing to be solved is the list of the users for the other tickets.
If the users for which the additional tickets should be created is static, then you can "hardcode" the user/contact into the sub ticket which are created by the Automation Rule.

If it's not static: How/Where do you want to specify for which users the additional tickets should be created?

Alternatively you could use a Smart Task (Admin > Tasks) which create a new ticket and inherits the settings of the mother ticket, except for the contact. By NOT using the "commit" checkbox and USING the "Open in new Window" checkbox, you only need to click on the Task, which will create a new ticket with all of the same settings but you'll have a chance to select a different contact.
--> Of course this does NOT create a batch, but a rather fast way to create those additional tickets but select the user manually for each sub ticket.