Most raised beds rest directly on top of the existing soil, lawn or hardscape, preventing soil from spilling out underneath. Is this not the case with yours?

If you do not have extra soil available of your own, bulk soil products available from many nurseries and landscape supply companies are your least expensive option. Check the yellow pages. Usually I recommend a 3-way planting mix but if you have quantities of compost, a good sandy loam (sometimes sold as topsoil) will suffice. Be aware that "topsoil" is a very generic term and I'd want to see it first. If you give them the dimension of the raised bed, they will calculate how much you need. Typically, most places will require a minimum order of at least 3 yards for delivery.

Gardengal48-

Yes, it will be on top of existing grass, but there are little low spots in the ground, dips where the ground is a few inches from the bottom edge of the structure. In the past I have tried to fill these in with soil and/or sod but they pack down and precious soil still spills out.

I have already turned over 6" into existing soil inside the bed, as well.

Also, sorry, but what exactly is a 3-way planting mix? Like soil, sand or pearlite, compost?
Thanks again.

Generally the area is leveled first or the bed form sunk to just slightly below ground level. If that's not possible, line the inner sides of the form with landscape fabric and allow it to fold into the bed at the base a few inches. That should stop most of the spilling.

3-way mix is typically some combination of loam/humus/topsoil, compost and sand. Perlite is not normally used in a raised bed or garden soil situation as it's a bit unnecessary as well as expensive. Better as an additive/amendment for container gardening.

Good suggestions here. I would also add a dark fabric ( sold at garden stores) that will not wash out readily.Mind you soil will always compact.You can add Pumicle ( garden stores) that will help drain it properly.Depending how deep you are going you could add some rocks on the bottom.I would add really good soil and if you are serious about gardening then you may want to add a composting bin.That way you can make your own compost.Good luck to you and enjoy...