When a Mode I crack in soft steel body grows and reaches near the perpendicular interface of ultra strong steel body, its cohesive zone penetrates into the interface body which influences the crack tip parameter. The paper presents finite element analysis of the cohesive zone across the interface of such elastically matched but strength mismatched bodies in linear elastic regime. Parent alloy steel (ASTM 4340) body and interface maraging steel (MDN 250) body are considered for analysis. The cohesive zone is modeled in accordance with the Dugdale criterion. J integral is evaluated over the path around the interface to examine the effect of cohesive stresses on the crack tip. The results are compared vis-à-vis those obtained from the theoretical model. The two are in very good agreement with each other.