Insulating basement walls with foam board (pink polystyrene)

[babebub]

Great video here once you get past the first 30 seconds.

A few points, the foam board has to be covered with a afire barrier in order to be safe and not violate building codes. Drywall does the trick just fine.

Also, a person could use a foam gun to seal all seams between each piece of foam board.
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The foam will seal the two pieces together better than caulk and the tape shouldn't be required. Also, make sure any foam board adhesive is put on the wall vertically (up and down). If it is applied horizontally it could prevent any moisture that enters from getting down to the floor where there is a drain tile, hopefully.