We ascribe the classical Forbush decrease (FD) as caused by the transverse flow of particles, which are undergoing essentially two-dimensional diffusion, to the 'sink' provided by the shock front and associated tangential discontinuity produced by a previous solar flare. The appropriate mathematical equations are solved to provide an analytical expression for the time profile of the FD, and by use of a Laplace transform we show that a quasi-equilibrium flow is set up very soon after the appearance of the shock front. The predicted profile is compared with neutron monitor records for individual events as well as with an 'average' event obtained by combining the profiles of 38 individual events. A test of the proposed mechanism is provided by the predicted dependence of the FD on the velocity of the shock front, and the individual events have been chosen so as to illustrate the effect of relatively fast and slow shock velocities.