Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singularpoints-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-leastsquares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.