Could someone help me with some ideas of how to design (Illustrator) something that is going to be stretched into a cylinder cartridge? For example a gas can, like you can see in this sample image from Web, some parts of the art stay flat - ie, the top part - while others will be stretched down and around the can, so i guess there's must be a technique for that and i have no idea which is it.
Similar to garment manufacturing, you must figure out how your shape will translate to a flat, 2D design.
Your example above can be designed with a circle for the top and a rectangle for the side.
When it comes time to wrap the flat image to the 3D shape you will need more info from the manufacturer about how the label machine prints the graphics. In the above example it may accept a circle and a rectangle separately and apply them to the cartridge, or it may require a radial shape that has the side printing distorted out into a large flat circle.
So on your own you can make the file by figuring out how the shape will translate to 2D, or go to the printer and ask them what shape or template is used to achieve this.
To preview or demo your graphics applied to the 3D shape you can use Illustrator extrude to make the cartridge and then map your label graphic around it.
Ask the specific provider (and this is very specific) about the process, he normally will provide a template for the specific model)
Besides that for a hypothetical design, you can probably use a 3D program and unwrap the model.
There are several methods to make this stuff. One is printing a flat sheet of metal and after is printed it receives a punch. But there are some other methods like water transfer print. So it is a bit hard to know the specific method used.