Do you know this?
An exercise was shown to me that is called Iron Ox Ploughs the Earth (Tie Niu Geng Di).

The starting position looks like you are doing a pushup, but during the exercise you flex your body from the waist in a sort of whipping action, so that your triceps doesn't take much load. The movement is circular and is harder on ones lower back and abdominals. The hands were shoulder width apart and the elbows went out (not parallel to your body) when the movement went downwards. When you look at it from the side, then the path is shaped like a "U", but it is much more flat.

I don't own the book, but one of the photos on the cover of Xingyi Neigong, looks similar to ending of one cycle. I was told that this is not it.

When typical Western push-ups use local muscle, then this style seems to try to use the whole body in the process. I have heard of an exercise with the similar objective used in Chen style taiji. I haven't seen this one, but it was supposed to teach you to apply jin through your arms.
One person called them rocking push-ups. Can anyone compare the Sun salutations with these?
Thank you in advance!

It was a major exercise among wrestlers in India. Can be done to combine strengthening and streching. Check the wrestling magizines and you can find several variations.

The Iron Ox pushups and the pushups in the Xing Yi Nei Gong book are basically the same. This is a very popular exercise. The Chinese call them Iron Ox Plows a Field, the Indian wrestlers call them Dand (cat stretching), American wrestlers call them Hindu pushups, the Brazilians call them scoops, the Marines call them dive bombers, the list goes on.

Thanks everyone!

Do the elbows remain parallel to the body or can they go out? Are the legs spread? How do the pushups that I described differ from the ones shown in the book?

I was shown some variations of this exercise on fingertips (straight fingers) and on fists, but it is really awkward to do them on fists.

In general, you don't want to open the elbows outward, you can do them with the feet close together or opened wide.