Abstract: When a star nears a supermassive black hole, the tides of the black hole can be sufficient to destroy the star, meaning that the tidal force of the black hole overwhelms the stellar self-gravity; this phenomenon of a star destroyed by tides is known as a tidal disruption event (TDE). Depending on the depth of the tidal encounter, i.e., depending on how close the star comes to the black hole, the tidal compression -- the same mechanism responsible for producing the low tides on the Earth -- can be extreme, and the star can be ``crushed'' into a small fraction of its original size by the tidal field of the black hole. Here we describe a model of such a deep TDE, and we demonstrate that previous, analytic estimates have significantly overestimated the maximum degree of compression experienced by the star. We present, make comparisons to, and find excellent agreement with very high-resolution, three-dimensional, hydrodynamical simulations of TDEs, and we provide an estimate of the minimum resolution needed to accurately capture the evolution of the compressing star in the deep-TDE regime. We also show that weak shocks (with Mach number <~ 2) can form and establish the maximum compression at sufficiently close distances. With time permitting, we discuss the extensions of our model to a general relativistic framework and the corresponding importance of general relativistic effects. These results have implications for exotic, thermonuclear transients generated by deeply plunging TDEs.