How can i soften the edges in the following way?
It is very important for me to get Softness only along the XY axis, without changing the dimensions of the Z axis. (sorry for my bad english)
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What you can do is select the left and right edge, as well as the top and bottom loop like so (make sure to do so while selecting edges, not faces):
Then, click N to bring up a tab on the right. Under Transform, set the mean crease to 1 like so:
Then, add a Subdivision Surface modifier to your object:
And you're done, your model should look something like this:
The smoother you want the object to be, the higher the View and Render number in the modifier should be.