Many applications require the sensing of plants. When an ultrasonic sensor insonifies a plant, the resultant echo is the superposition of the echoes from the leaves. As a result, the echo contains information about the geometric structure of the foliage. In this paper, we present a model of sensing that facilitates the extraction of geometric features from the echo for plant classification, recognition and discrimination. We model the echo from a CTFM ultrasonic sensor with the acoustic density profile model. Then, we identify a set of features that represent plant geometric characteristics and use these to perform an inverse transform from echo features to plant geometry.