LEGS has posted some excellent examples of yama-tsuki applications, and LeonardoBJJ's suggestion of a high block and body punch is also good. Something to keep in mind is that "tsuki" doesn't mean "punch," it means "thrust." All that means is that you are forcefully extending your arms--what you do with that motion is up to you. Also, people tend to think that "double" motions in kata must always be done simultaneously, but their timing can actually be staggered. With those things in mind, it's much easier to look beyond the simple "double punch to the face and body" idea for yama-tsuki.
While I am open to a variety of applications, my preference for yama-tsuki is to use it to cut the lines of my opponent's attack while countering--preferably while also jamming any following attacks from them. By that, I mean that one of the arms is going to cut into the path of my opponent's punch, effectively blocking it, while maintaining the option to strike. Here is a traditional karate example of this:
Now, right off the bat, I can tell you that I don't like the way this is presented, but that isn't really important. What is important is the concept being shown. You can see that, against the first punch, the demonstrator drops his left arm over the top of a low punch in such a way that it deflects it, while still allowing him to strike with it. Against the second punch, his right arm lifts and twists so that it pushes the attack out of the way, while leaving his hand in a position to strike the face. Now, you most likely will never do both of these things, because people don't generally throw two punches like that, but again, the concept is what I'm looking at here.
For a more practical look at the karate method, we can consider this example from Motobu Choki's book, Okinawa Kenpo Karate-Jutsu: Kumite-Hen. Motobu Choki was known for routinely getting into fights in rough areas of town to test his karate, generally had a reputation for practical karate and cross-training, and even took up a challenge match against a Western boxer, winning by knockout. In other words; the man knew how to fight. In the example, above, he shows how you can throw a punch on the inside of your opponent's punch so that it deflects it, while allowing you to strike at their face. He then follows up by throwing a knee to the body, and you'll see that he has control of both arms when he does it--we'll get to that in a bit.
In case you think this is just a karate idea, here is the very same concept illustrated by Jack Dempsey in his book, Championship Fighting, as well as in his fight against Jess Willard. He calls the technique on the left a "glance-off," and the one on the right a "right corkscrew," but they are both really using the same concept--you throw a strike in such a way that it acts as both a deflection and a punch.
Now, to make this a yama-tsuki, simply use your non-striking hand to check your opponent's free arm. In Motobu's demonstration, he is keeping his right hand in its guard position (the old-school karate "guard" posture was essentially the same as Western bareknuckle boxers') while throwing his line-cutting strike. In Dempsey's examples, he simply keeps his non-striking arm out of the way. If they used their free hand to reach out and check their opponent's other arm, they would end up in the same posture as yama-tsuki. It also leaves you in an excellent position to tie up the opponent's arms and throw knees, as Motobu shows, or simply tie them up, because you are already in contact with both of their arms.
