This document proposes a simple transmission line model for analyzing a patch antenna placed on a metamaterial substrate. The metamaterial substrate is modeled as a sandwich of a double negative material between two double positive materials. The transmission line model divides the patch into three sections, with an equivalent transmission line used to model each dielectric section. Input impedance calculations show the antenna exhibits multiple resonances when using the metamaterial substrate, with the number and spacing of resonances depending on the proportion of double negative material used. Comparisons with a numerical model show the transmission line model provides a reasonable approximation.