We present a numerical code for calculating transient flow in plastic pipes, especially in the polyethylene pipe, to analysis transient flow in a viscoelastic pipe such as polyethylene. The set partial differential equations to be solved is obtained using conservation laws and behavior for the fluid and the pipe wall, associated with constitutive equations of the two media. A global digital processing is achieved using the method of characteristics. The results obtained are in good agreement with those found in the literature.