Exact closed-form stress intensity factor (SIF) solutions have been developed for a mode- I through-thickness cracks in an infinite plate. Centre-crack problems have been analysed comprehensively in the literature, but the focus has been on the effect of simple loading about the crack centre. In the current work, the formula of Sih-Paris-Erdogan has been extended to consider the SIF difference on the left and right crack tips, under the local influence of general asymmetric and symmetric stress field. Exact SIF magnification factors convenient for computations have been derived that simultaneously circumvent the problem of crack-tip stress singularity. The solutions so obtained are applied to generate the residual SIFs that would act on a crack growing under the influence of the residual stress fields associated with welded plates and cold-worked holes using the measured residual stress profiles.