A. Bill Rose, architect and building researcher at the University of Illinois Urbana-Champaign, responds: Ideally, insulation should be installed on the exterior of your basement wall, but it is probably too late for that. If the soil at your site is very well drained and dry, then it is a fair thermal insulator, and (energy codes aside) you might consider omitting the drywall, and simply painting the interior walls with epoxy paint.
Assuming the client insists on interior insulation, there is no clear answer on the question of where to put a vapor barrier. Condensation usually occurs when moist air encounters a cold surface. You could argue for a vapor barrier on the inside of the insulation (assuming the foundation wall is cold), or on the foundation side of the insulation...
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