The method of lines (MOL) has been applied to the solution of multiphase hydrodynamic equations describing the flow of gas and solid particles in vertical pipes. These sets of equations, which are hyperbolic, are traditionally difficult to handle numerically. They were successfully solved using FORSIM, a program package that implements the method of lines. Solutions have been obtained for one-dimensional transient model. Using this numerical technique, the propagation of continuity wave is predicted by the one-dimensional transient model.