In this paper, numerical solution of hypersingular integral equations in curved-crack problems is presented. The stress fields induced by two kinds of standard sets of force doublets are used as fundamental solutions. Then, the problem is formulated as a system of integral equations with the singularity of the form γ^-2. In the numerical calculation, two kinds of unknown functions are approximated by the products of the fundamental density functions and power series. The calculation shows that the present method gives rapidly converging numerical results for curved cracks under various geometrical conditions. In addition, a method of evaluation of the stress intensity factors for arbitrary-shaped curved cracks is proposed using the approximate replacement with a simple straight crack.