Eshelby’s energy-momentum tensor and Rice’s $J$-integral provide path-independent measures of configurational forces driving defects and cracks in elastic media. Their applicability, however, breaks down in materials where distributed anelastic rearrangements screen elastic stresses over a screening length $|\kappa {|}^{-1}$. Here, we generalize these constructs to mechanically screened media dominated by dipolar screening. We identify two distinct regimes associated with real and imaginary $\kappa$, leading to qualitatively different responses. Real screening induces exponential attenuation of elastic fields, and in the context of cracks, suppresses energy flow into crack tips, resulting in effective toughening. In contrast, imaginary screening produces spatially oscillatory fields that enhance energy transport, promoting fragility. Our results extend the foundational tools of fracture mechanics to screened elastic media and reveal new regimes beyond classical linear elastic fracture mechanics.