Abstract The reactivity effect of spatial random dispersal of core materials was analyzed in the framework of one-group diffusion theory by the time-eigenvalue method, and in the framework of two-group diffusion theory by both the time- and the reactivity-eigenvalue methods. The analysis based on one-group diffusion theory leads to that spatial random perturbations in the macroscopic cross sections and/or the diffusion coefficient cause the positive reactivity effects under the assumption of zero ensemble-averages of these perturbations. However, the analysis based on two-group diffusion theory shows that the algebraic sign of the reactivity depends upon the reactor types and the buckling. A specific example in which spatial noise causes the negative reactivity was also shown.