The dynamics of solar magnetic flux ropes are investigated. The model starts with an equilibrium flux rope which contains a low-density hot component and a denser cold component, qualitatively resembling a prominence cavity with an embedded prominence. The ''eruption'' of the entire flux rope is triggered by an increase in the poloidal magnetic flux of the structure. The subsequent expansion of the flux rope through a model corona and solar wind is analyzed using macroscopic quantities, including the forces, apex speed and height from the Sun, and magnetic field. The computed flux rope properties are in good agreement with those of observed magnetic clouds. On the basis of these results, magnetic clouds are identified as the interplanetary counterpart of the magnetic field and plasma of the initial cavity. The dense cold component, although drained out near the Sun, significantly influences the resulting magnetic structure in the heliosphere. After a cloud passes 1 AU, it is found that the magnetic field strength of the flux rope at 1 AU continues to decrease and that the magnetic energy in any finite heliocentric sphere vanishes as ~t-1 even with zero resistivity, where t is time. The cumulative magnetic energy inside the 1 AU sphere associated with repeated eruptions of flux ropes is calculated.