If there is no phone number on the invitation to respond to and the invitation says "The favor of a reply is requested" does that mean you have to hand write a response?

Blueeyes

I would think this depends on the formality of the invitation, as well as your relationship to the person issuing you the invite. If a close friend, call and ask. If not, reply with either the enclosed response card or a short handwritten note.

Normally on a formal invitation, a written resonse if proper

Not necessarily. They could be assuming that you know the number or could have inadvertently forgotten to include it.

You can send an invitation cards (http://www.123greetings.com/invitations/) thanking the person to invite you and also give the reply in that.