A non-local elliptic equation, for which comparison methods areapplicable, associated with Robin boundary conditions is considered. Upperand lower solutions for this problem are obtained by solving algebraic equations. These upper and lower solutions are used to obtain analytical boundsfor the critical (blow-up) parameter of the problem. Numerical results arepresented for the slab, cylindrical and spherical geometries. The results arecompared with the existing ones in the literature.