The problem of a V-notched isotropic elastic half-plane under generalized plane stress or plane strain conditions can be reduced, by using the complex variable technique, to a complex Cauchy type singular integral equation along one of the V-notch edges. This equation can be numerically solved by use of the Gauss-Jacobi method and reduction to a system of linear equations. The values of the stress intensity factorKI at the V-notch tip were evaluated for some notch angles in the case of pure tension and the results obtained are in accordance with the available results in the case of a V-notched finite isotropic plane elastic medium. The difficulties faced in evaluatingKI are investigated and a discussion on them is made. The method is also applicable even when the V-notch edges are curvilinear and their loading arbitrary.