WEAVE is an approved massive wide field multi-object optical spectrograph (MOS) currently entering its build phase, destined for use on the 4.2-m William Herschel Telescope (WHT). It will be commissioned and begin survey operations in 2017. This paper describes the core processing system (CPS) system being developed to process the bulk data flow from WEAVE. We describe the processes and techniques to be used in producing the scientifically validated 'Level 1' data products from the WEAVE data. CPS outputs will include calibrated one-d spectra and initial estimates of basic parameters such as radial velocities (for stars) and redshifts (for galaxies).