Proper growth and function of plant roots are critical for crop production. The study of root systems to elucidate their link to production is expensive and labor intensive. The use of computer simulations, both to summarize existing knowledge of root system growth and to guide research promises to speed our understanding of the complex interdependence of the crop root and shoot systems. Of the many factors restricting root penetration into the profile, soil strength is perhaps the most difficult to describe and measure. We propose to compute with general elastic theory a soil-imposed resistance to root penetration using an elastic modulus for the soil. The application of the theory to agricultural soils is discussed and the specific application to root expansion in a soil cylinder is developed. Computations of root length density profiles and root depth over time in both uniform and layered profiles with known elastic modulis are provided as examples of predicted root growth based on this theory.
