The development of soil penetration devices has been the focus of large technological efforts due to the richness of material and energy resources in the soil. Therefore, much effort has been invested in order to attain efficient sensing and searching capabilities. Plant roots are considered the most efficient soil explorers among living organisms. As opposed to the penetration strategy of other organisms, that is based on pushing through soil, roots penetrate by growing, adding new cells at the tip and elongating over a well defined growth zone. This growth-based strategy provides anchorage and minimal lateral friction, has been adopted in a recently developed plant-inspired self-growing robot. Currently, however, the physics underlying growth-driven penetration in soil is not well understood, preventing significant advancement of plant-inspired robots and other penetration devices. Here we propose to develop a computational model describing the mechanical characteristics of growth-driven penetration of plant roots in soil, to explore the mechanical interaction of the root during its growth into the medium and to compare it with a simple penetrometer-like mechanism. We also suggest to identify the mechanical mechanisms by which a penetrating object can sense an obstacle remotely via mechanical forces transmitted in the medium (as is observed in mechanical sensing of animal cells). We experimentally validate our model using displacement measurements of growing roots and a pushed needle in the medium. These findings will pave the way for a new generation of root-inspired growing robots with efficient penetrations and searching capabilities.