I assume you are making these to fit around the tables so that they won't slip or blow off in wind outdoors? Sort of like a fitted sheet?
You can sew through any narrow elastic with a wide zigzag, and I'm pretty sure that would be easier than making a casing and - heaven help you! - pulling it through several of them. I used to sew a lot of little swim suits for my daughter that had elastic around all the openings. The instructions were in patterns of that era (25- 30 years ago). If you know how long the finished circle of elastic needs to be, you can cut it to that length plus a little more. Overlap and sew it securely in a circle using a zigzag stitch. Then pin it along the edge you need to attach to. Do this by first folding the tablecloth in half, marking the fold points with pins. Then fold it again in half the other way, matching the first two pins to find the centers. Then again, find the centers between the pins you already have in place.
Now you're going to mark the elastic the same way. Safety pins might make this whole process simpler if the pins tend to slip out, or you can skip the pins and just make marks with a wash-out pen. Then it's a matter of matching your marks. Pin the elastic with one mark matching one on the tablecloth. Then gently stretch the elastic the full distance between the pins while you zigzag in place. It will be tricky at first to do this without breaking a needle, but the technique is to have one hand holding the material behind the needle and the other at the next pin or mark and letting the fabric feed with the elastic on it at the machine's pace, not fighting it. You will be stretching the elastic, but not the fabric, if that makes any sense. It might be good to practice on something small.
Also, just yesterday I learned about this foot
http://www.stitchntimeinc.com/shop/B...RD-x663805.htm which I have not tried, but maybe it's the solution you need.