No.2. in Yang’s 10 Important Points is “Sink the chest and pluck up the back”.

Yang says: “2.) Sink the chest and pluck up the back. The chest is depressed naturally inward so that the ch’i can sink to the tan-t’ien [field of elixir]. Don’t expand the chest: the ch’i gets stuck there and the body becomes top-heavy. The heel will be too light and can be uprooted. Pluck up the back and the ch’i sticks to the back; depress the chest and you can pluck up the back. Then you can discharge force through the spine. You will be a peerless boxer.”

Personally, I like thinking of it as ‘shelter’ the chest, rather than “sink” or “hold in”, even if that’s not the exact translation. I think that works better in English for me, it implies a more natural position with less force being used than ‘hold in’ does. YMMV.

The whole thing is intimately related to the breath and ‘sinking the chi to the dantien’. If you change the focus of the breathing to the dan tien area, so that area expands when you breathe in and contracts when you breathe out (that’s ‘normal’ dan tien breathing, there’s reverse as well, but let’s not get into that) then your upper chest will natural soften and have the feeling of hollowing – so it’s not so much something you actively ‘do’, it’s more like something that happens as a result of doing something else. The old Wu Wei idea of doing without doing. The whole posture in Tai Chi should be as natural as possible without any artificial additions – but it does require effort (including mental effort) to do, paradoxically – you have to make an effort to be as relaxed as possible, usually by getting rid of the unnatural habits we pick up through doing things like typing on this computer or misusing our bodies in other ways, such as stiff shoulders and neck.

If you let the upper chest expand as you perform the movements then you are effectively ‘letting the chi rise up’ rather than ‘sinking it to the dan tien’. In Tai Chi you need to make your centre of gravity the dan tien area, and this requires letting the tension in the upper body release downwards (of course, you still need that opposite feeling of being drawn upwards from the crown that’s talked about in the classics, and in the above quote as “pluck up the back”, otherwise you slump, or get that crumpled ‘old man’ look I see too often in Tai Chi practitioners, which is not good either IMHO).

One of the meanings of chi is air, or breath, so you can see how ‘sinking the chi to the dantien’ relates to breathing from that area, and how ‘letting the chi rise up’ relates to the breath being too high in the body. All the posture requirements of Tai Chi (as featured in Yang Cheng-Fu’s 10 Important Points essay) are all part of the same thing really, so it can sometimes be misleading to consider them on their own as separate things – or as Mike Sigman said:

In relation to the tail-bone tuck (which I think really just says that the tail-bone should point downward and says nothing about “tuck”), one way of looking at that requirement is that it’s for the same reason the gua is sunk and relaxed, the back is relaxed, the head is suspended, the armpit is rounded, the crotch is rounded, the chest is hollowed and the back rounded slightly, and the stomach is relaxed. They are all done to affect the same thing which connects them all.

All this being said, there are a wide variety of interpretations of what these things mean amongst the different styles. Amongst Tai Chi stylists (mainly from Yang Lu Chan lines, since Chen guys seem to want to be a law unto themselves  ) I think my view above is by far the most common IMHO, but you can counter pose it with the view amongst some Bagua stylists that the chest should be expanded outwards, but this seems to be part of a complete system and way of doing things that is very complete and detailed, and includes circulating energy in directions counter to the more usual way of doing it.