As the hart panteth after the water-brooks. Stags and hinds need abundant water, especially in hot countries, and, in time of drought, may be said, with a slight poetical licence, to "pant," or "cry" (Joel 1:20) for it.
They are still found in Palestine, though rather scarce. So panteth my soul after thee, O God. The "panting" of the soul does not mean any physical action, but a longing desire for a Messing that is, at any fate for a time, withheld.