  This paper shows that an analytic space $X$ has a unique maximal model
through which every proper surjective morphism from a non-singular analytic
space to $X$ factors. This is called the {\sl geometric minimal model} of $X$
and characterized by the contraction property of rational curves. Some other
properties such as functoriality, the direct product property and the quotient
property of the geometric minimal model are also studied here. The relation of
the geometric minimal model with Mori's minimal model is discussed.
