In this paper we investigate the Sunyaev-Zeldovich (SZ) effect and the X-ray surface brightness for clusters of galaxies with a non-spherical mass distribution. In particular, we consider the influence of the shape and the finite extension of a cluster as well as of a polytropic thermal profile on the Compton parameter, the X-ray surface brightness and on the determination of the Hubble constant. We find that the the non-inclusion of such effects can induce errors up to 30 per cent in the various parameters and in particular on the Hubble constant value, when compared with results obtained under the isothermal, infinitely extended and spherical shape assumptions.
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