For integrity evaluation of cracked or damaged structures, fracture toughness test results in ASTM are widely used. The fracture toughness values of the structures are used as an effective design criterion in nuclear plants and aircraft structures. Sometimes the difference of P-$delta$ curve trend during the unloading /reloading cycle in the fracture toughness test using partial unloading compliance was observed. The phenomenon as a possible source of error in determining fracture toughness may be caused by the residual stress during unloading work-hardening and bucking of a specimen. Therefore, we evaluate the effect of bucking and compressive residual stress during the K-R and J-R testing using a finite element method.