Roots system is vitally important organ for a living plant.One of the major functions of the root system is taking water and nutrients from soil.Water is first transported from soil to the root surface and taken up by plant roots; it is then transported to the stems and leaves along the xylems tubes of the roots,which located in the central part of root inside the Caspian strip.In this paper,we shall develop a mathematical model for the dynamical process of the water uptake of a single steadily growing plant root.We shall use small Reynolds number,creeping flow to describe water motions outside the root,and use Poiseuille flow to describe the water transport along the vascular tubes inside the root.The resulted system of partial differential equations are studied under different growth conditions,The features of mathematical solutions are discussed.