Singular integral equations have been applied to the quasistatic growth of an edge crack in an isotropic elastic half-plane when a self-balancing load is given at the crack edges. The path has been calculated by a step method with allowance for the stress redistribution during the crack growth, and the growth direction has been determined from the σθ criterion. The resulting singular integral equation is solved numerically by mechanical quadratures. Paths have been constructed and stress intensity coefficients have been determined for them for uniaxial stretching of a half-plane at infinity and also for normal pressure and localized forces applied to the edges of an initially rectilinear but arbitrarily oriented crack. Some trends in edge break-away are identified.