I created five "flags" and placed them on a yellow rectangle. Each of the flags and the yellow rectangle are on their own layer, but then I created a new layer that combines everything into one, and turned off the visibility of the individual layers.
Now go to Edit>Transform>Warp. In the drop-down box, select "Arc" and set the Arc Bend to 100%. You'll get a half-circle, like this.
Repeat this process for the bottom half (different flags) by setting the Arc Bend to
negative 100%. Then you can join the two shapes to form a clean circle.
Creating an ellipse is a bit trickier. In the Warp command, you can set the bend amount to something less than 100%, but then the top and bottom won't join cleanly. Another option is to first make the circular version and then flatten it to an ellipse using Edit>Transform>Scale.
