  The superconducting transition in presence of strong columnar disorder
parallel to the magnetic field is considered. A solvable model appropriate for
description of the broad crossover regime towards the true "glassy" critical
behavior is constructed, and the behavior of the thermodynamic quantities and
of the Edwards-Anderson order-parameter is obtained. The critical exponents for
the correlation lengths orthogonal and parallel to the magnetic field are equal
and in agreement with the experimental values. The dynamical critical exponent
is $z=2$, also in agreement with the measured value. Several perturbations to
the solvable model are considered and shown to be irrelevant for the critical
behavior. It is argued that there exists an optimal density of defects at which
the transition temperature at given magnetic field reaches its maximum.
