Have you ever went to the river to try and catch a timid trout only to spook it time and time again because you cannot get you fly to the target area without disturbance? Then this cast is what you need.
Technically not a fly fishing cast but an aerial line mend the reach mend allows a lot of slack fly line to be introduced to the fly fishing cast so you can present a fly without any drag during the drift downstream. When learnt correctly it allows the fly fishing angler to add the mend to the fly line before the fly hits the water so there is no disturbance to it from that point on and you maximize your casting drift for potential takes.
If however you perform the mend when the]fly line hits the water you are going to move the fly unnaturally for a moment which can spook timid trout as you already know. Once mastered reach mend fly casting will provide you with the technique to cast without the need to water mend again. This cast can be performed on both arms on your dominant casting shoulder or over your none casting shoulder.
Technique for right handed fly anglers
Once you make the stop on the forward cast let out a little fly line as it shoots forward then reach (hence the name of the cast) out as far as you can with your rod to the right as you need to. If casting from the left bank upstream water is to your right as a right handed angler you would reach to your right upstream to allow the line to be placed upstream and slow the drift down and not cause motion on your flies.
Technique for right handed fly anglers over none casting shoulder
If on the right hand bank with left being the river upstream you would forward cast to the stop then let some line slip then reach as far as you can left upstream over your none casting shoulder to leave the fly line upstream, to allow the drag free drift.
This cast makes the act of mending so simple and can bring you many trout. The art of presenting flies to waiting and feeding fish is more satisfying when your casting causes little or no disturbance and you can see your fly disappear with a swirl as your line tightens.
Thanks to bumcast for the video below explaining the reach cast in detail.