Fault close to tunnel always plays an important role to the stability of surrounding rock mass and the safety of supporting system in underground excavation engineering, and presents diverse influencing features and severity under the condition of these initial stress distributions with different lateral pressure coefficients related to geology tectonic structure. Systematic numerical tests have been carried out to investigate the stability of surrounding rock mass with a fault on right sidewall, under the condition with initial stress featured with 5 different lateral pressure coefficient (0.38, 1.0, 1.5, 2.0 and 3.0 respectively), and the safety situation of the supporting system also has been analyzed via the maximum compressive and tensile stress in sprayed concrete layer. COJO element, an interface element to simulate fault behavior, has been introduced and used in all numerical tests. Some quantificational results on the fault influence to the stability of tunnel surrounding rock mass are summarized the under the five conditions respectively, especially the displacement, stress, plastic region in surrounding rock mass, and stress in sprayed concrete layer by comparing these cases without a fault around tunnel.