  We address a problem of the upper critical field in a lattice described by a
two-dimensional tight-binding model with the on-site pairing. We develop a
finite-system-approach which enables investigation of magnetic and
superconducting properties of electrons on clusters, consisting of a few
thousand sites. We discuss how the quasiparticle density of states changes with
the applied external magnetic field and present the temperature dependence of
the upper critical field. We also briefly discuss possible extension of the
model to account for the properties of high-temperature superconductors.
