ESPRESSO is the next generation European exoplanet hunter, combining the efficiency of a modern echelle spectrograph with extreme radial velocity and spectroscopic precision. The instrumental radial velocity precision will be improved to reach 10 cm/s level, to achieve a gain of two magnitudes with respect to its predecessor HARPS. The fiber-fed, non-rotating instrument will be installed in the Combined Coudé Laboratory of the VLT (Very Large Telescope), which is situated in the Paranal Observatory (Chile). The main challenge in the design of the optical mounts of the instrument has been the extreme long-term stability of big rectangular optical components in a seismic environment. This paper describes the requirements and the adopted solution for the opto-mechanical design of the collimator mirrors, dichroic lens, field lens and cross dispersers of the instrument.