Some of the best experiences I've ever had on the Yakima involve the Green Drakes. Seeing the smartest, biggest and baddest fish on the river lose their minds over this bug is something all anglers should experience. The fish that never eats on top, the big smart ones that sit on the bottom in heavier flows and give you the fin repeatedly. They lose all sense of fear and feed recklessly, rising in fast lanes that you might not fish if you didn't see that toad levitate off the bottom and go airborne. That's a sight to hold on too.
The hatch itself can be difficult to accurately predict, the best approach is to stay on the water as much as possible and keep looking for nymphs via the old school method: turning over rocks or using a seine. One of the Largest of all the mayflies, a size 10 parachute on the surface can keep you laughing and giggling all day. Keep in mind, this hatch is strongest above the Cle Elum river confluence, and in the Cle Elum river proper. The grey and brown Drakes also make an appearance, can be amazing, has a larger range then the Green's, but doesn't seem to hold the fish's (and angler's) attention as much.
The Green Drake must taste better...