[en] This report displays the theory of the spatial burnup computer code ''UAFCC'' which has been constructed as a part of an integrated reactor calculation scheme proposed at the Reactors Department of the ARE Atomic Energy Authority. The ''UAFCC'' is a single energy-one-dimensional diffusion burnup FORTRAN computer code for well moderated, multiregion, cylindrical thermal reactors. The effect of reactivity variation with burnup is introduced in the steady state diffusion equation by a fictitious neutron source. The infinite multiplication factor, the total migration area, and the power density per unit thermal flux are calculated from the point model burnup code ''UABUC'' fitted to polynomials of suitable degree in the flux-time, and then used as an input data to the ''UAFCC'' code. The proposed burnup spatial model has been used to study the different stratogemes of the incore fuel management schemes. The conclusions of this study will be presented in a future publication. (author)