The integral transport equation is solved in periodic slab lattices in the case where a critical buckling search is performed. First, the angular flux is factorized into two parts: a periodic microscopic flux and a macroscopic form with no angular dependence. The macroscopic form only depends on a buckling vector with a given orientation. The critical buckling norm along with the corresponding microscopic flux are obtained using anisotropic collision probability calculations that are repeated until criticality is achieved. This procedure allows the periodic boundary conditions of slab lattices to be taken into account using closed-form contributions obtained from the cyclic-tracking technique, without resorting to infinite series of exponential-integral evaluations. Numerical results are presented for one-group heterogeneous problems with isotropic and anisotropic scattering kernels, some of which include void slit regions.