The structure of the spectrograph ESOPO is the stiff mount that will maintain fixed all optics elements, electronics and mechanical subsystems. The ESOPO spectrograph is a project of the "Instituto de Astronomia de la Universidad Nacional Autonoma de Mexico" (IAUNAM) to upgrade its 2.1m telescope as a competitive facility for the next decade. The scientific purpose is to obtain a modern high efficient intermediate-low dispersion spectrograph optimized for the 3500 - 9000 a spectral interval with a spectral resolution of 500 ≤ R ≤ 5000. It is to be used at the cassegrain f/7.5 focus of the 2.1 m telescope for general astronomical purposes. This work presents the mechanical design process and the form in which the structure was verified to comply with the ESOPO's top level image quality and stability requirements. The latter was not a lineal process. The way we resolved it is to run FEAs on the complete system and with the instrument in different operation positions during a normal cycle of observations. These results are validated through the error budget of the ESOPO. The structure is currently under construction.