The rigorous three-dimensional theory for a TAP (Temporal Analysis of Products) Knudsen pulse response experiment is developed for the combined diffusion and reaction cases for multi-zone packing, in order to determine the domain of validity of the commonly used one-dimensional model. The analysis is based on a specific modification of the transfer matrix formalism previously introduced for one-dimensional TAP-reactor models. The outlet flux can be written as a sum of three independent terms: one corresponding to the one-dimensional solution, a term accounting for axially symmetric radial nonuniformity, and a term needed for a fully three-dimensional model. The theory provides a method for estimating the accuracy of the one-dimensional model and For finding the domain of its validity. The theory is illustrated by the diffusion-only case for a one-zone reactor, it is shown that the one-dimensional model is valid for aspect ratios L/R > 3.5.