We study the transverse stability of solitary waves on a system of coupled nonlinear electrical transmission lines. In the continuum limit, and in suitably scaled coordinates, the voltage on the system is described by a modified Zakharov-Kuznetsov equation. Exact results for the growth rate of linear transverse perturbations are obtained by applying the technique of multiple-scale analysis due to Allen and Rowlands. Comparisons are made with numerical results obtained with the aid of a commercial circuit simulation package.