In order to preserve the structural integrity against brittle fracture, structural materials should be selected based on the proper evaluations of the fracture toughness of materials and of the near tip field parameters of a crack by an appropriate stress analysis. In welded structures there exist some difficulties in achieving the procedure. The precise evaluation of the fracture toughness of materials is not a simple task, if a welding process induces the spatially distributed inhomogeneous material degradation such as the locally restrained decrease of the fracture toughness in the heat affected zone. Considering a brittle crack initiated and propagating along a welded joint, it sometimes exhibits sharply curved paths and penetrates into the base material, while in other cases it propagates in a straight fashion along the welded joint. It is clear from these observations that the prediction of brittle crack paths is essential for the evaluation of fracture toughness of welded structures. In the present paper a mathematical model is proposed for the crack path prediction, in which the combined effects of applied stresses, welding residual stresses, and material degradation in the so-called heat affected zone are taken into account. In the present model a homogeneous fracture toughness is assumed in both the base and weld materials, where the crack path is predicted by the local symmetry criterion ( K _II =0) based on the first order perturbation solution of a slightly kinked and curved crack. When a curved crack propagating in a weld material intersects the heat affected zone which is modelled as a line degradation zone, a quastion arises as to whether the crack extends along the heat affected zone, or whether it penetrates into the base material. Since the local symmetry criterion does not work at this point, the crack growth direction is predicted by the minimum principle of the total potential energy. The relevant energy calculations can easily be performed by using the second order perturbation solution of a kinked crack. Numerical results show that if brittle fracture occurs under a relatively low applied stress in comparison with the longitudinal welding residual stress, and if the average material degradation along the heat affected zone is small, crack paths tend to deviate from the welded joint. This is the case actually observed for brittle fracture of welded plates made of mild steel, where cracks extend in the base material. It is also shown that cracks tend to propagate along the heat affected zone with increasing the applied stress and materials degradation levels, which may possibly simulate certain brittle fracture of welded plates made of high tensile steel.