We study the influence of intensive internal gravity waves, which are generated from baroclinic tidal wave and disturbances related to the variations in atmospheric pressure, on the hypothetic pillars of marine structures. We use temperature and salinity vertical profiles from GDEM climatology in a region near the Zohr offshore natural gas field located in the Egyptian sector of the Mediterranean Sea. Investigation of internal waves' dynamics was carried out in the framework of program complex intended for numerical modelling of propagation and transformation of such waves in the ocean, that implements procedure of numerical integration of fully nonlinear two-dimensional (vertical plane) system of equations of hydrodynamics of inviscid incompressible stratified fluid in the Boussinesq approximation bearing in mind the forcing by barotropic tide. The variations of the horizontal and vertical velocities are studied. Morison's formula is used to calculate the pressure force on the lateral surface of the elongated cylinder (pile). In the framework of this approach flow pressure contains the inertial (linear, depending on the acceleration of fluid particles in the wave) and the drag (non-linear resistance force, quadratic in velocity) components. It is shown that the inertial force is mainly smaller in absolute value than the drag force. A distribution of the loads and torques upon unit length of the pillar in time is considered.