  The Helfand-Werthamer (HW) scheme\cite{HW} of evaluating the orbital upper
critical field is generalized to anisotropic superconductors in general, and to
two-band clean materials, in particular. Our formal procedure differs from
those in the literature; it reproduces not only the isotropic HW limit, but
also the results of calculations for the two-band superconducting
MgB$_2$\cite{MMK,DS} along with the existing data on $H_{c2}(T)$ and its
anisotropy $\gamma(T)=H_{c2,ab}(T)/H_{c2,c}(T)$ ($a,c$ are the principal
directions of a uniaxial crystal). Using rotational ellipsoids as model Fermi
surfaces we apply the formalism developed to study $\gamma(T)$ for a few
different anisotropies of the Fermi surface and of the order parameters. We
find that even for a single band d-wave order parameter $\gamma(T)$ decreases
on warming, however, relatively weakly. For order parameters of the form $
\Delta(k_z) = \Delta_0(1+\eta\cos k_za)$,\cite{Xu} according to our simulations
$\gamma(T)$ may either increase or decrease on warming even for a single band
depending on the sign of $\eta$. Hence, the common belief that the multi-band
Fermi surface is responsible for the temperature variation of $\gamma$ is
proven incorrect.
