How to round edges when using Solidify

[BorisBoev]

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!

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[muhuk (Atamert Ölçgen)]

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)