Summary: \(J^{\text{ep}}\)-integral is derived for characterizing the fracture behavior of elastic-plastic materials. The \(J^{\text{ep}}\)-integral differs from Rice’s \(J\)-integral in that the free energy density rather than the stress working density is employed to define energy-momentum tensor. The \(J^{\text{ep}}\)-integral is proved to be path-dependent regardless of incremental plasticity and deformation plasticity. The \(J^{\text{ep}}\)-integral possesses clearly clear physical meaning: (1) the value \(J^{\text{ep}}_{\text{tip}}\) evaluated on the infinitely small contour surrounding the crack tip represents the crack tip energy dissipation; (2) when the global steadystate crack growth condition is approached, the value of \(J^{\text{ep}}_{\text{far-ss}}\) calculated along the boundary contour equals to the sum of crack tip dissipation and bulk dissipation of plastic zone. The theoretical results are verified by simulating mode I crack problems.