Defitely stretchy, but not really sticky. My kids have some floral tape (sometimes called stem wrap tape) from a craft project they worked on. To use it you just put a little tension in the tape as you wrap it multiple times around the stems you want to join. The tape tries to shrink back to shape after it wrapped, and in doing so it holds the stems together. The tape is thin so it really isn't that noticecale. I've seen it in brown and green but when used on scenery projects it sounds like most models prefer to paint it more of a gray color to match a tree trunk.
We got ours at Michaels.