This article presents the synchronisation criteria for a class of dynamical networks with each node being resistively-capacitively-inductively-shunted (RCL-shunted) Josephson junction, which guarantee the synchronised states to be global asymptotically stable. These conditions are established in terms of linear matrix inequalities (LMIs), readily solvable by available numerical software. In addition, an interesting conclusion is reached that the stability of synchronisation in the coupled whole 3N-dimensional networks can be converted into that of 3-dimensional space.