At CERN, a high performance negative ion (NI) source is required for the 160 MeV H β linear accelerator named Linac4. The source should deliver 80 mA H β ion beams within an emittance of 0.25 mmΒ·mrad. For this purpose two ion sources were developed: IS01 is based on the NI volume production and IS02 provides additional NI by surface production via H interaction on a cesiated Molybdenum plasma electrode. The development of negative ion sources for Linac4 is accompanied by modelling activities. ONIX code has been modified and adapted to investigate the transport of NI and electrons in the extraction region of the CERN negative ion sources. The simulated results from modeling of IS01 and IS02 extraction regions, which were obtained in 2012 during source commissioning, are presented and benchmarked with experimental measurements obtained after 2013. The formation of the plasma meniscus and the screening of the extraction field by the source plasma are discussed. The NI production is compared between two types of sources, the first one based on volume production only and the second one encompassing NI cesiated surface production. For the IS02 source, different states of conditioning were simulated by changing the NI emission flux from the plasma electrode and Cs + density in the bulk plasma region. The numerical results show that in low work function regime, with high NI surface emission rate of 3000 A m β2 and Cs-density of n Cs+ =ο 3.8 Γ 10 16 m β3 , the total extracted NI current could reach~80 mA. At the less favorable Cscoverage, when the surface NI emission rate becomes significantly lower, namely 300 A m β2 with n Cs+ =ο 3.3 Γ 10 15 m β3 , the total extracted NI current only reaches~20 mA. A good agreement between simulation and experimental results is observed in terms of extracted NI current for both extraction systems, including the case of reversed extraction potential that corresponds to positive (H + ) ion extraction.