The technique of crack extension is applied to the computation of critical stress intensity factor in linear elastic fracture mechanics for cracked plates in tension for different crack configuration (i.e. central crack, edge crack, and double edge crack). The new technique uses the Brown approximate solutions for stress intensity factors and the Westergaard analytical solutions for stress and displacement near a crack tip in finite plate to calculate crack extension during each load step and then calculating the critical stress intensity factor using an incremental procedure. A matlab program was developed for the purpose of this work, which proved to be a good tool for the computation of critical stress intensity factors for cracked plates. The results were in good agreement with results of other methods available in the literature.