In/on

The "in" one.

Both are fine and common, PJ.

British usage would never use the "on" form, FWIW.

A Google search produces 3,030,000 hits for 'on the elevator' at .uk domains. It is obviously in reasonably common use in the UK. Here are some:

Offer name tags to everyone getting on the elevator.

By this time we were on the elevator and he said he was going up to homicide and robber

Would we create motion sickness by subjecting riders on the elevator

The word elevator is, in itself, American English. We use the word lift. You will find this discussed on almost any place dealing with US versus UK usage: it's one of the basics.

"On the elevator" or "on the lift" would sound wrong when used over here. The standard phrase would be, "In the lift." You would never be "on the lift" - that would sound to us like you are standing on top of th