Yes, you can, but generally not 100% memory foam. Because this type of foam adapts to heat, it will compress with your body heat, and sink further with increased pressure. Because Shiki futons are fairly thin, 1.5 to 4 inches thick generally, memory foam tends to thin in such futons. Our #6 is an example of this: the 3” thick Colorful Mart Japanese futon, which has a memory foam top layer. Needless to say, this mattress cannot be flipped, but it can be rotated.