The displacement field in the casing satisfies the thick The Seismic Borehole Problem is an up-to-date and shell kinematic approximation and the equilibrium written important issue whose numerical modeling is rather in the weak sense for any displacement field satisfying complex because it involves several major difficulties: an the same kinematic assumption: intermediary frequency range where neither finite differences nor ray methods seem best suited, a large ratio between borehole diameter, casing thickness and dimensions of surrounding formation without it being possible to ignore their respective influences, prevailing heterogeneous conditions: fluid, casing and soil formation.