  Joint analyses on X-ray and Sunyaev-Zel'dovich (SZ) effect of a cluster of
galaxies can give rise to an estimate on the angular diameter distance to the
cluster. With the redshift information of the cluster, the Hubble constant
$H_0$ can then be derived. Furthermore, such measurements on a sample of
clusters with a range of redshift can potentially be used to discriminate
different cosmological models. In this paper, we present statistical studies on
the systematic errors in the determination of $H_0$ due to the triaxiality and
non-isothermality of clusters of galaxies. Different from many other studies
that assume artificially a specific distribution for the intracluster gas, we
start from the triaxial model of dark matter halos obtained from numerical
simulations. The distribution of the intracluster gas is then derived under the
assumption of the hydrodynamic equilibrium. For the equation of state of the
intracluster gas, both the isothermal and the polytropic cases are
investigated. We run Monte Carlo simulations to generate samples of clusters
according to the distributions of their masses, axial ratios, concentration
parameters, as well as line-of-sight directions. To mimic observations, the
estimation of the Hubble constant is done by fitting X-ray and SZ profiles of a
triaxial cluster with the isothermal and spherical $\beta$-model. We find that
for a sample of clusters with $M=10^{14}h^{-1}\hbox{M}_{\odot}$ and $z=0.1$,
the value of the estimated $H_0$ is positively biased with
$H_0^{peak}(estimated)\approx 1.05H_0(true)$ and $H_0^{ave}(estimated)\approx
1.05H_0(true)$ for the isothermal case. For the polytropic case with
$\gamma=1.15$, the bias is rather large with $H_0^{peak}(estimated)\approx
1.35H_0(true)$ and $H_0^{ave}(estimated)\approx 3H_0(true)$. (abridged)
