  Solar prominence models used so far in the analysis of MHD waves in such
structures are quite elementary. In this work, we calculate numerically
magnetohydrostatic models in two-dimensional configurations under the presence
of gravity. Our interest is in models that connect the magnetic field to the
photosphere and include an overlying arcade. The method used here is based on a
relaxation process and requires solving the time-dependent nonlinear ideal MHD
equations. Once a prominence model is obtained, we investigate the properties
of MHD waves superimposed on the structure. We concentrate on motions purely
two-dimensional neglecting propagation in the ignorable direction. We
demonstrate how by using different numerical tools we can determine the period
of oscillation of stable waves. We find that vertical oscillations, linked to
fast MHD waves, are always stable and have periods in the 4-10 min range.
Longitudinal oscillations, related to slow magnetoacoustic-gravity waves, have
longer periods in the range of 28-40 min. These longitudinal oscillations are
strongly influenced by the gravity force and become unstable for short magnetic
arcades.
