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Isostasy states that the weight of a column of crust and lithosphere is balanced by buoyancy from the mantle, so the crust 'floats' on denser mantle material. Airy isostasy predicts a deeper root beneath mountains and shallower crust under ocean basins; Pratt isostasy explains topography through lateral density variations. Elastic lithosphere flexure extends isostatic theory to account for the finite strength of the lithosphere under applied loads like seamounts or sediment.
From your study of gravity anomalies and plate tectonics, you know that the Earth's gravity field reflects mass distribution beneath the surface, and that the lithosphere is broken into moving plates riding on a ductile asthenosphere. Isostasy connects these ideas by explaining why high mountains have deep roots and why the crust responds to loading and unloading over geological time. The simplest analogy is blocks of wood floating in water: a tall block (a mountain) extends deeper below the waterline than a short block (a plain), and if you place a weight on top, the block sinks until buoyancy balances the added load.
Airy isostasy formalizes this floating-block model. It assumes the crust has uniform density but varies in thickness — mountains are high because they have thick crustal roots extending into the denser mantle. The Himalayas, for instance, are underlain by a crustal root reaching 70 km or more, compared to the global average of about 35 km. The key equation is a pressure balance: at a compensation depth deep in the mantle, the total weight of each vertical column of crust-plus-mantle must be equal. If one column has a tall mountain on top, it must have a correspondingly deep, low-density root displacing heavy mantle rock to maintain the balance.
Pratt isostasy offers a complementary explanation. Instead of varying thickness at constant density, Pratt's model keeps the base of the crust at a constant depth and explains topographic differences through lateral density variations. Higher elevations correspond to lower-density crust; basins correspond to higher-density material. In practice, both mechanisms operate: the Andes have thick roots (Airy) while mid-ocean ridges are elevated partly because their hot, young lithosphere is less dense than old, cold oceanic lithosphere (Pratt). Real isostatic analysis uses gravity anomalies — specifically the difference between observed gravity and what you would predict from visible topography — to distinguish regions in isostatic equilibrium from those that are not.
The Airy and Pratt models both treat the lithosphere as if it has no strength — each column floats independently like a separate block. But the lithosphere is an elastic plate, and it distributes loads over a wider area. When a volcanic island like Hawaii builds up on the ocean floor, the lithosphere does not simply sink beneath the island — it flexes downward in a broad depression around the load and bulges upward in a peripheral ring called a forebulge. The characteristic distance over which this flexure occurs is called the flexural wavelength, and it depends on the elastic thickness of the lithosphere. Thick, cold, strong lithosphere distributes loads over hundreds of kilometers; thin, hot, weak lithosphere deforms more locally. Flexural isostasy explains features like the moats around oceanic islands, the foredeep basins in front of mountain belts, and the pattern of postglacial rebound — regions like Scandinavia and Hudson Bay are still rising today, centuries after the ice sheets melted, because the viscous mantle flows back slowly to restore isostatic equilibrium.