[paintedlady]

I used cardboard last year on 3 new raised beds for potatoes, covered with cheap plastic weed suppressing sheet and put compost over the top.  

Top tips - make sure the soil is dug over at least once to break it up and mix in manure (and maybe some extra feed such as fish, blood & bone if the soil is pretty poor - up to you what you need).  Make sure the soil is moist (water it well if dry), sprinkle some slug pellets over the soil before covering with cardboard.  Cover with the black plastic weed suppressant sheet (was about £3 from T*sco and covered 3 raised beds - it has tiny holes to allow water through) and weight it with bricks or some of the soil to stop the wind whipping it off.  Leave it a few days (preferably when sunny) and the soil warms up lovely.  Use a sharp dibber to pierce plastic & card and pop spuds in.  Backfill hole with compost and cover the rest of the bed with a thin layer of compost (this aids water to seep through the plastic otherwise most of it will run off)  When harvesting, most of the potatoes were near the surface - I had very little slug damage, no green potatoes and a lovely crop (I grew some Anya, Kestrel & Foremost)

Advantage - no weeding throughout the growing season, most of the cardboard had rotten and dug in with the compost after harvesting and the bed was immediately ready for an overwintering crop.  I'll definitely be trying it again this year.  

[woodburner]

I've heard of potatoes on cardboard (I grew them that way last year) but not the other way round.
I've also heard of growing them under black plastic so I guess it could work. Personally I wouldn't have plastic anywhere near my spuds or anything actually growing as it is an absolute haven for snails.

I think there must be a good reason for mounding up the stems, as it is done even when whole fields are involved. I suppose it might just be cheaper/easier than putting out miles of plastic, definitely easier than cardboard. :shock:  I used straw to mound up to start with and finished off with spare topsoil from elsewhere in the garden. Grass clippings would have done except that the grass wasn't growing enough to need cutting.