<p>We report for the first time a rigorous, first principles derivation of the Additive Flow Resistance (AFR) model for wall-flow Particulate Filter (PF) backpressure prediction, which was first proposed by Konstandopoulos and Johnson (SAE Technical Paper 890405). Originally, this model/equation was not derived from first principles but rather is an empirical correlation obtained by fitting data. The AFR model is so called because backpressure is given as the sum of the individual flow resistances (across the PF wall, across the soot cake, along the inlet channel and along the outlet channel). The derivation involves analytic solution of the momentum balance equations for the case where the inertial terms are negligible, followed by a power series approximation. The assumptions used to derive the AFR model inform us of when the model is likely to be valid, viz. when inertial contributions to backpressure are negligible and when the pressure drop across the PF wall and soot cake is large compared with that along the channels. Separation of the effect of individual flow resistances into separate, additive terms in the AFR model equation is the result of an approximation; in reality, individual flow resistances are not separable but are intrinsically linked.</p>