SPHERE (Spectro Polarimetric High contrast Exoplanet REsearch), the planet finder instrument for the VLT is designed to study relatively bright extrasolar giant planets around young or nearby stars. SPHERE is a set of three instruments fed by the same AO-system, two of them share the same coronagraph. This complex system has been modeled with Fourier Optics to investigate the performance of the whole instrument. In turns, this end-to-end model was useful to analyze the sensitivity to various parameters (WFE, alignment of the coronagraph, differential aberrations) and to put some specifications on the sub-systems. This paper presents some example of sensitivity analysis and some contrast performance of the instruments as a function of the flux for the main observing mode of SPHERE: the Dual Band Imaging (DBI), equivalent to the Spectral Differential Imaging technique.© (2008) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.