A possible discrepancy found between the determination of mass of the intracluster medium (ICM) from gravitational lensing data and that from X-ray observations has been much discussed in recent years. For instance, Miralda-Escudé & Babul found that the mass estimate derived from gravitational lensing can be as much as a factor of 2-2.5 larger than the mass estimate derived from analysis of the X-ray observations. Another important discrepancy related to these data is that X-ray imaging, with some spectral resolution, suggests that the mass distribution of the gravitating matter, mostly dark matter, has a central cusp, or at least that the dark matter is more centrally condensed than the X-ray-emitting gas, and also with respect to the galaxy distribution (Eyles et al.), at variance with what is expected from the most accepted models of formation of large-scale structure. Could these discrepancies be a consequence of the standard description of the ICM, in which hydrostatic equilibrium maintained by thermal pressure is assumed? In analogy to the interstellar medium of the Galaxy, a non-thermal term of pressure is expected, which contains contributions of magnetic fields, turbulence and cosmic rays. We follow the evolution of the ICM, considering a term of magnetic pressure, aiming at answering the question of whether or not these discrepancies can be explained via non-thermal terms of pressure. Our results suggest that the magnetic pressure could only affect the dynamics of the ICM on scales as small as <~1kpc. Our models are constrained by the observations of large- and small-scale fields, and we are successful at reproducing available data, for both Faraday rotation limits and inverse Compton limits for the magnetic fields. In our calculations, the radius (from the cluster centre) in which magnetic pressure reaches equipartition is smaller than radii derived in previous works. The crucial difference in our models is our more realistic treatment of the magnetic field geometry, and the consideration of a sink term in the cooling flow which reduces the amplification of the field strength during the inflow. In addition, the magnetic field calculations are changed after the cooling flow has been formed.