In cases where successive integration of F(x) is not practical, a solution of the equation d2y/dx2=F(x) is obtained by approximation. The solution attempted is to find the value of y at selected points in the range of integration. A common procedure is to reduce the problem to the solution of a set of linear simultaneous equations, and these equations are then solved by “relaxation”. It does not appear to be generally known that an explicit and simple solution of these simultaneous equations exists. In this note the detail of such a solution is carried out for functions F(x) as occur in the theory of thin beams.