Crushing is a non-elemental hazard in the Pikmin series. While soft-bodied Pikmin that get crushed die right away, Rock Pikmin can withstand the weight, although Winged Pikmin are also mostly immune to being crushed.
Pikmin have weak bodies that cannot resist most forms of crushing forces, except for Rock Pikmin. Once a Pikmin is crushed, it becomes flat in whatever direction it was crushed, then disappears with a soul, with no way to save it. However, Rock Pikmin merely become partially buried in the ground and unharmed, and must be left to unearth themselves automatically after some seconds. The time it takes for them to unearth does not depend on their maturity and is random between six and eleven seconds.
Leaders are not immune to crushing either. If a leader is crushed, they will become flat for a second, and slowly return to their original size. Being crushed normally causes considerable damage, and the prolonged damage animation may allow the leader to be hit by a different attack while they are unable to react.
Interestingly however, Winged Pikmin can't get crushed by anything but the Quaggled Mireclops and the crystal cubes from the Plasm Wraith: these attacks will just push Winged Pikmin away, even if they are grounded.
In Pikmin and Pikmin 2, crushing can be identified by the distinct sound Pikmin make when killed. In Pikmin 3, any attack that a Rock Pikmin can survive by becoming buried counts as a crushing attack.
Ways to get crushed
Although the Mamuta crushes Pikmin into the ground with its hands, this does not count as a crushing hazard, as this is actually beneficial to the Pikmin. It's still harmful to leaders, however. In addition, the Quaggled Mireclops has some attacks that trample Pikmin, killing them in the process, but this is a fatal attack that Rock Pikmin are not immune to.
The rough exterior of Rock Pikmin gives them the ability to survive crushing attacks, making them quite valuable when fighting enemies that pose a crushing hazard. However, Rock Pikmin won't completely ignore crushing attacks like other Pikmin types ignore attacks of the hazard they are invulnerable to: they become temporarily and partially buried.
There is a glitch in the first two Pikmin games where an enemy or a certain object will crush a Pikmin abnormally, when it isn't even meant to crush in the first place. Very rarely, an object on top of a Pikmin will make said Pikmin vanish.
Yellow Wollywog corpse crushing
As seen in a trailer for Pikmin, it appears that in a development version of the game, Yellow Wollywogs could crush Captain Olimar's army during their death animation, where they tense up and fall to the side. In the final game, this does not happen, except unintentionally, with the aforementioned glitch.