I found this question in an Amazon.com customer discussion area. The question is:
We get questions about memory foam mattresses and box springs or foundations very frequently.
A memory foam mattress can absolutely be placed on a traditional box spring. What used to be called a box spring is now generally called a foundation. It is for this very reason that we do not even sell foundations for our memory foam mattress. Most people can use their existing foundation or box spring for their new memory foam mattress. It is a great way to save money. Unless your existing foundation or box spring is trashed and needs to be replaced, save it for your new memory foam mattress.