The so-called dissipative model [i, 2] has recently found wide use when describing unsteady flow of a compressible fluid in circular pipes.The solution of particular problems of unsteady flow of a compressible fluid in pipes on the basis of the dissipative model presents certain mathematical difficulties, since the classical method of separation of variables is not applicable here, and on using the operational method there are difficulties in inverting the transforms of the solution. Therefore, the solutions of particular problems on the basis of this model were obtained mainly by means of the method of approximate inversion of the Laplace transform for small times [2,5].The Kantorovich variational method together with the numerical finite-difference method is used in this article for solving the problem of unsteady fluid flow in a pipe. As in [4,5], by means of the variational method integration of the system of differential equations for a function of three variables is reduced to integration of an infinite system of differential equations for a function of two variables. The solution of this system is expressed by one integrodifferential equation. The finite-difference method is used for solving the latter equation.The temporal change of the velocity components at different points of the cross section of the flow and change in the average velocity and pressure are found by the described method for the initial stage of fluid flow upon a rapid drop of pressure at one end of the pipe. (5) (6)where S, ~, T are dimensionless coordinates and us, u~, q are dimensionless parameters determined by means of the relations