We investigate a monolithic algorithm to solve the problem of time
dependent interaction between an incompressible viscous fluid and an
elastic solid. The continuous formulation of the problem and its
discretization is done in a monolithic way, treating the problem as
one continuum.  The Q2/P1 finite elements are used for the
discretization and an approximate Newton method with coupled multigrid
linear solver is developed for solving the equations. We discuss
possible efficient strategies of setting up the resulting system and
its solution.  A 2-dimensional configuration is presented to test the
developed method. It is based on the older successful DFG benchmark
flow around cylinder for incompressible laminar fluid flow.  Similar
to this older benchmark we consider the flow to be incompressible and
in the laminar regime.  The structure is allowed to be compressible or
incompressible and the deformations of the structure are periodic and
significant in terms of displacement.  This configuration can be used
to compare different numerical methods and code implementations for
the fluid-structure interaction problem qualitatively and particularly
quantitatively with respect to efficiency and accuracy of the
computation.