How to pass a soft object through a narrow channel? I found an excelent Q/A about Some examples of shape key sculpting vs lattice?. @moonboots suggests in his answer to use a Lattice in order to deform an cylinder object:

How does that work? How can I pass a soft object through a narrow channel like @moonboots does in his answer?
What you've posted there is no soft object passing through a channel, it's actually a Cylinder with a Lattice Modifier moving through a Lattice object.

Add a Cylinder to your scene or whatever object you want to deform.
To be deformed smoothly it needs enough geometry, so subdivide it either in Edit Mode or with a Subdivision Surface modifier.
Add a Lattice to your scene (Shift+A &gt; Lattice)
In the Lattice settings, set the Resolution W to at least 3.
Go to Edit Mode and scale the middle vertices down so that they narrow the Lattice in the center.
Add a Lattice Modifier to the Cylinder and under Object choose the Lattice.
Now you can move the Cylinder up and down and it gets deformed.

EDIT: I'm too slow. The above solution is correct, this is just a shorter version.