This paper presents the study of modelling root growth behaviours in the soil. The purpose of the study is to investigate a novel biologically inspired methodology for optimization of numerical function. A mathematical framework is designed to model root growth patterns. Under this framework, the interactions between the soil and root growth are investigated. A novel approach called "root growth algorithm" (RGA) is derived in the framework and simulation studies are undertaken to evaluate this algorithm. The simulation results show that the proposed model can reflect the root growth behaviours and the numerical results also demonstrate RGA is a powerful search and optimization technique for numerical function optimization.