Drawing from the advantages of Classical Mechanics, the peridynamic theory can clarify the crack propagation mechanism by an integral solution without initially setting the factitious crack and crack path. This study implements the peridynamic theory by subjecting bilateral notch cracked specimens to the conditions of no local damage, small radius local damage, and large radius local damage. Moreover, to study the effects of local stochastic damage with different radii on the crack propagation path and Y-direction displacement, a comparison and contact methodology was adopted, in which the crack propagation paths under uniaxial tension and displacement in the Y-direction were compared and analyzed. This method can be applied to steel structures under similar local random damage conditions.