Deformation and fracture processes in pre-cracked graphene sheets are examined by molecular dynamics simulations. Thin and thick pre-existent cracks in graphene sheets are considered which are generated through removal of one and two (neighboring) chains of carbon atoms, respectively, from a pristine sheet. Tensile tests of graphene sheets with these cracks oriented along zigzag directions were performed. Crack evolution/growth processes were observed and described. Also, for each graphene sheet tested, we revealed stress-strain dependence, maximum elastic strain, maximum plastic strain, and tensile strength.