This contribution presents the structural analysis that followed the preliminary design specifications of the European Solar Telescope (EST). EST is a 4-metre class telescope based on an aplanatic Gregorian configuration with an alt-azimuthal mount. The optical design has undergone several changes since the end of the conceptual phase. A finite element model (FEM) was developed to verify the structural performance of the telescope with the new optical design. This model includes the elevation structure, the azimuth platform, the pier and the ground at the observatory site. Two different orientations of the telescope were modelled, pointing horizon and zenith. Dynamic modal analyses were performed to estimate the natural frequencies and mode shapes of the telescope. Gravity, wind and thermal static analyses were used to compute the displacements and rotations of the optical elements. These deformations were then combined with the optical sensitivity matrix. The sensitivity matrix relates displacements and rotations of the optical elements with the image motion at the focal plane. The performance of the new optical design in terms of image motion and its impact on the technical specification was made. These analyses were used for defining the specification of the preliminary design in terms of eigenfrequencies and image motion.