Capillary penetration of liquids in porous and fibrous materials is of practical importance in many industrial processes such as textile and paper treatment, detergency, and filtration, and for environmental matters such as penetration of oil in sand or rocks, In the proposed experiment, a piece of fabric is put into contact with a wetting liquid. The mass of liquid absorbed is recorded as a function of time, The dynamics of capillary rise is compared to the classical Washburn law observed in the case of a porous membrane. The kinetics measured cannot be described with a simple Washburn law involving a single capillary radius. We present experimental evidence for simultaneous imbibition processes of the fabric : (i) a volume imbibition inside the strands of yarn, which are shown to behave as an assembly of capillary tubes and (ii) a surface rise, due to the alveoli formed by the woven structure of the fabric, The system thus appears as a double porous medium, characterized by two different sizes, Exchange of matter between the two media is possible but in our case we show that imbibition can be simply described by two independent processes,