We outline here a new analytical model of the global evolution of powerful extended radio sources. On the basis of hydrodynamic simulations of propagating jets we approximate a radio lobe as a set of co-axial cylindrical slices that evolve and expand independently and sideways only. From the law of energy conservation we derive the evolution of different forms of energy and synchrotron emission locally, for individual slices, and globally, for the lobe as a whole. We find that the source transversal expansion values for plasmas dominated either by thermal matter or by relativistic particles are similar. We notice epoch-dependent radiation efficiency, luminosity stabilization for old sources and departures from energy equipartition. The model predicts that many observed radio sources stay at the same internal stage in their evolution, since differing values of model parameters yield different evolutionary patterns only for relatively young objects. We also stress the importance of a geometrical description of the radio lobe, and show that our geometrical approach leads to certain results convergent with models based on different geometrical and physical presumptions.