The propagation of magnetic clouds in the interplanetary medium between the Sun and Earth is studied using two different numerical methods. No numerical method can account completely for the complexity of the physical processes that occur in the solar wind because approximations need to be made. In solving the time-dependent MHD equations, a number of simplifications and assumptions are made. These may have significant influence on the results obtained. We compare the results of two-dimensional simulations obtained from two different MHD codes based on different numerical methods, namely, the two-step Lax-Wendroff and the total variation diminishing Lax-Friedrich numerical schemes. The two codes give similar results, which are in general agreement with observational data. The numerical results are then compared with analytical solutions of an evolution of a flux rope published by Osherovich et al. [1995> and applied to magnetic clouds. It follows from this solution that the polytropic index &ggr; must be less than 1 in order for a cloud to expand, i.e., as is observed. Polytropic index &ggr;>1 allows only for oscillations of the cloud. In the present paper it is shown that under the same conditions, the analytical solution and the numerical code give the same results, but when more realistic initial conditions are used, the modeled magnetic clouds behave differently. ¿ 2000 American Geophysical Union