Abstract: In this paper, the solution, more general than [1], of a weak singular integral equation subject to constraint is found where k and F are given continuous functions: (s,) is a local polar coordinatingwin origin at M(r,θ): (r) is the global polar coordinating with origin at O(0,0) F(r_*, θ)=c_*(const) is the boundary contour ∂Q of the considered range and N are mean values. The solution shown in type (2.19) of [1] is a special case of theabove solution and only suits F(r,θ) = ω. The solution of a rigid cone contact withelastic half space. more simple and clear than Love’s (1939), is given as an example ofapplication.