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If you map that particular one as a flat "perfect" rectangle, especially if you use patterns, it will be stretchy, due to the mismatch between the size of the top and the bottom.
but yes - there are absolutely ways to map cylindrical shapes as rectangles.
If you're working with Blender, it works best if they're meshed as square polys, so you'll first want to convert the triangles into squares. In most cases, marking all the faces and clicking J will do so, but you'll have to go over the mesh to see if everything is in place, because the auto tool will very often remove the wrong edges, depending somewhat on the mesh you're working with. Marking edges you want to remove, then doing X+"Dissolve edges" can also work.
You also need to make sure you've made a seam along one side of the cylindrical shape. If there's an inside and outside, cut those apart and map them separately (but keep the seam along the same line). I usually try to hide that seam where it's not going to be too visible, so wherever the back of the mesh is most likely going to be is the best place.
Then you can follow these directions:
https://www.youtube.com/watch?v=bHbgQs8zkpw
It's not perfect - you will likely have to do some more adjustments for the size/shape of the individual segments.
I've seen some programs have spesific cylindrical-to-rectangle mapping, but haven't found anything like that in the earlier version of Blender I'm working with (2.76). It's possible the later versions have better UVmapping tools.
There are a few other ways suggested here, too:
https://blender.stackexchange.com/q...aighten-uv-maps