  A simple variational model is proposed to analyze the superconducting state
in long cylindrical type-II superconductor placed in the external magnetic
field. In the framework of this model, it is possible to solve the
Ginzburg-Landau equations for the states with axially symmetric distributions
of the order parameter. Phase transitions between different superconducting
states are studied in the presence of external magnetic field and an
equilibrium phase diagram of thin cylinder is obtained. The lower critical
field of the cylindrical type-II superconductor with arbitrary values of radius
and Ginzburg-Landau parameter is found. The field dependence of the
magnetization of thin cylinder, which can carry several magnetic flux quanta,
is calculated.
