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,φ) is a local polar coordinatingwin origin at M(r,θ): (r,θ) 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 Q:g(ω)=F(r,θ)/[πkφ₀];g'=dg/dω,ω=N-r²sin²(θ+φ₀);φ₀ 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 with elastic half space, more simple and clear than Love's (1939), is given as an example of application.