Abstract: A new formulation is provided for the fundamental problem of elastic half-plane with arbitrary cracks．By using proper decomposition of the functions and elimination‚the problem is reduced to Riemann-Hilbert’s boundary value problem on cracks．The stress functions of elastic body are obtained in closed form of integral expression and the stress intensity factors on the tip of cracks are also derived．

Key words: cracks, Riemann-Hilbert’s boundary value problem, stress intensity factor