A one piece foam mattress core or innerspring encasement is a single contiguous piece of foam having a mattress core or base and four perimeter side supports and which fits with a mattress core or innerspring to provide an integrated mattress construction. The mattress core or base of the encasement is positioned below the mattress core or innerspring proximate to or against a bottom surface. The mattress core or base and the perimeter side supports are connected along fold lines or grooves in the single piece of foam so that the perimeter side walls can be folded to vertical positions about a perimeter of the mattress core or innerspring. The single piece of foam of the encasement is producible in different sizes to fit with different size mattress cores or innersprings.