First of all – a thickness of foundation sheet itself (refer to question on foundation sheets’ production). In addition, stiffness largely depend on time which has been passed since its production.
Fresh sheets are the softest, but after just a few days passed, – these reaches 50% of their stiffness, becoming apparently much more sturdy. However, a full recrystallization process for wax takes place within next few months. Therefore, it is advisable to put older embedded sheets into hives, even of last years’ production, rather than those freshly made.