Flat Yagi antenna Enclosure
If I understand you well, your problem is that the shape of the enclosure of the antenna is cylindrical. (Or is the antenna wound up for transport/storage?) If the antenna is used lying on a table, you could attach (glue) two little light plastic or paper pieces to it to prevent it from rolling.

Some general remarks: All plastic materials have a dielectric constant that modifies the behavior of the antenna. The only neutral zone is the boom, if it is located in the centre. There it does not matter if it is conductive or not. Putting plastic material around each element of the antenna (radiator, reflector, director) would definitely change the behavior of the antenna. The same holds for putting anything along the ends of these parts. If the antenna is usable as is, better leave it like this.