In analogy with the pom-pom model, we introduce a simple model for comb polymers with multiple side-arms attached to a linear backbone by considering a set of coupled equations describing the stretch in the individual interbranch backbone segments. The stretch equations predict a sudden onset of backbone stretch as the flow rate is increased. Drag-strain coupling smooths this transition to some extent. For a series of well characterized polyisoprene and polystyrene combs, we find good agreement with the experimentally determined transient stress growth coefficients in uniaxial extension. (C) 2014 The Society of Rheology.