Non-woody plants (also called Herbaceous plants or herbs) are plant with a relatively short-lived shoot system . (compared to woody plants). 
Most angiosperms lack a vascular cambium, i.e., they are non-woody herbs or herbaceous.

Non-woody plants:

• Herbs: There are several types of herbs, including:
  • Forbs: Broad-leaved herbs.
  • Graminoids or grass: Grass-like herbs, with very narrow  leaves. .
  • Ferns: Herbs with broad but highly dissected leaves and no flowers.
• Herbaceous vines: Non-woody plants that climb on other plants.

Most cacti and  succulents are herb.