ESPRESSO is a new generation, super stable, high-resolution optical spectrograph, conceived to obtain the best performance in Doppler shift measurements. A concept study of the instrument is being carried out by a Consortium of scientific institutions formed by ESO, OG, IAC, INAF and Institute of Astronomy in Cambridge, all of them leaded by ESO (see Pasquini et al., these proceedings). Within this framework, the optomechanical, mechanical, and thermal conceptual design of ESPRESSO is being developed by engineers at the IAC. This contribution presents an overview of the current optomechanical conceptual design of this spectrograph.