How to round edges when using Solidify

Hi all!
I learn Blender to use for 3d packaging render.
I already made 3d model from 2d vector draft but stuck with Solidify modifier.
My model has no thickness and I want to add it using Solidify modifier with Offset=0.
How to make round edges with this modifier? Please look at the picture below.
Or there are other easy ways to do it?
Thank you very much!


Do you have two objects there?

I took a cube, deleted top & bottom faces, then applied solidify and then bevel on it:

Actually, just to check, the edge nearest to camera is a split edge result still seems to be satisfactory.

Here is the modifier stack:

(You would probably want to apply smooth shading of course, I did not for clarity)