  We outline here the motivation for the existence of analytic QCD models,
i.e., QCD frameworks in which the running coupling $A(Q^2)$ has no Landau
singularities. The analytic (holomorphic) coupling $A(Q^2)$ is the analog of
the underlying pQCD coupling $a(Q^2) \equiv \alpha_s(Q^2)/\pi$, and any such
$A(Q^2)$ defines an analytic QCD model. We present the general construction
procedure for the couplings $A_{\nu}(Q^2)$ which are analytic analogs of the
powers $a(Q^2)^{\nu}$. Three analytic QCD models are presented. Applications of
our program (in Mathematica) for calculation of $A_{\nu}(Q^2)$ in such models
are presented. Programs in both Mathematica and Fortran can be downloaded from
the web page: gcvetic.usm.cl.
