We explore here the structural stability and fracture of supported graphene sheets under pressure loadings normal to the sheets by performing molecular dynamics simulations. The results show that, in absence of defects, supported graphene deforms into an inverse bubble shape and fracture is nucleated at the supported edges. The critical pressure decreases from ideal tensile strength of graphene in biaxial tension as the size of supporting pores increases. When nanoscale holes are created in the suspended region of graphene, the critical pressure is further lowered with the area of nanoholes, with additional dependence on their shapes. The results are explained by analyzing the deformed profile of graphene sheets under pressure and the stress state.