  We study the problem of the upper critical field ($H_{c2}$) for tight-binding
electrons in a two-dimensional lattice. The external magnetic field is
introduced into the model Hamiltonian both via the Peierls substitution and the
Zeeman term. Carrying out calculations for finite systems we analyze the
influence of the external field in the commensurable and incommensurable case
on an equal footing. The upper critical field has been discussed for intrasite
as well as anisotropic intersite pairing that, in the absence of magnetic
field, has a $d_{x^2-y^2}$ symmetry. A comparison of $H_{c2}$ determined for
different symmetries shows that the on-site pairing is more affected by the
external field i.e., the critical temperature for the on-site pairing decreases
with the increase of the magnetic field faster than in the anisotropic case.
Moreover, we have shown that the tight-binding form of the Bloch energy can
lead to the upward curvature of $H_{c2}$, provided that the Fermi level is
close enough to the van Hove singularity.
