A model is developed for the rate of elongation of a root tip in terms of the balance of pressures acting on the root. Differentials of this equation give expressions for the changes in root elongation rate with respect to soil water potential and soil mechanical resistance. The model predicts that root cells osmoregulate against both water stress and soil mechanical resistance with predicts that root cells osmoregulate against both water stress and soil mechanical resistance with similar efficiencies which are less than 100%. Analysis of published data leads to the conclusion that root tips of pea osmoregulate with 70% efficiency. A working equation is developed for the elongation rate of roots in conditions of combined water stress and mechanical resistance.