  We describe a non-parametric method to reconstruct gas density and
temperature profiles of galaxy clusters from observations of X-ray surface
brightness, emission-weighted temperature and the y-parameter through the
Sunyaev-Zel'dovich effect. This method is based on the inversion of the
projected profiles under the spherically symmetric approximation, which is
independent of the equation of state of cluster gas and does not assume that
the gas is in hydrostatic equilibrium. In particular we examine the reliability
of the reconstruction method assuming a few theoretical models for cluster gas
and assigning the statistical errors expected for future X-ray and radio
observations. We also discuss briefly the effect of non-sphericity on the basis
of simulated clusters.
