The 2 x 2 tubular cast-on gives a very firm but stretchy edge to your knitting. It is meant for an edging that is knit 2, purl 2 ribbing.
Start with two circular needles: the needle that gives the correct gauge for the project, and a needle one size smaller than the “gauge” needle. The needles will be held side-by-side (with the smaller needle on the bottom).
Make a slipknot and put it on the smaller needle.
Now wrap the yarn around both needles. Wrap under the gauge needle and then over both needles.
Then continue to wrap around both needles. The number of wraps is one-half of the number of cast-on stitches.
Next, knit in stockinette for a few rows across the “top” of the wraps on the gauge needle.
To make the knitting easier, pull the tip of the smaller needle so that only the smaller needle’s cord is holding the stitches on the bottom.
Now the “tops” of the wraps can be knit without the extra thickness of the smaller needle’s tip.
Only 3 rows of stockinette are needed for this cast-on. This swatch shows 5 rows to make it easier to see what’s going on.
Pull the smaller needle’s tip back into the stitches.
Here is where the magic happens. The stitches on the gauge needle will be the purls in the 2 x 2 ribbing. The stitches on the smaller needle will be the knits in the 2 x 2 ribbing.
The fabric is folded so that the purl sides face each other. The gauge needle’s stitches will be in the back and the smaller needle’s stitches in the front.
Note: The setup below (p1, k2, p2, …) is for when the knitting will be joined in the round after the cast-on is complete. In other situations, like a button band, it might be more appropriate to start p2 from the gauge needle, then k2 from the smaller needle, and repeat.
Start the ribbing by purling 1 stitch from the gauge needle. Then knit 2 stitches from the smaller needle. Now purl 2 stitches from the gauge needle. Repeat the knit 2, purl 2 process until the last stitch on the gauge needle. Purl this last stitch.
And now the stitches can be joined to work in the round!