How to laminate or hold together somewhat thick posters?

I am doing a speech, with posters that are fairly thick.. At least thick enough that they cannot be put through our school's laminating machine. Each time I give the speech, they get beat up, and the letters and pictures on it keep coming off and getting bent. Is there anything I can do about this? I can't seem to find any self-adhesive laminating sheets that are large enough... Help? Ideas? Experience with this?