  The Mostar index of a graph was defined by Do\v{s}li\'{c}, Martinjak,
\v{S}krekovski, Tipuri\'{c} Spu\v{z}evi\'{c} and Zubac in the context of the
study of the properties of chemical graphs. It measures how far a given graph
is from being distance-balanced. In this paper, we determine the Mostar index
of two well-known families of graphs: Fibonacci cubes and Lucas cubes.
