This paper proposes a modification to the shear lag model for multiple cracking of thin films in order to take into account the residual strain, and uses it to estimate the critical fracture strength of SiOx films with thicknesses from 75 to 660 nm deposited on 12 thick polyethylene terephthalate (PET) substrates. It was found that : (1) The difference of residual strains in the film and substrate increased as the thickness of the film decreased. (2) In both initial and multiple formation of cracks, SiOx films failed at almost constant values of a critical stress ranging from 200 to 300 MPa when the thickness was larger than 200 nm, whereas below that it failed at higher values.