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The dispersion law for the linear waves in the quasi-one-dimensional array ofinductively coupled Josephson junctions (JJ) is derived. The array has amultiladder structure that consists of the finite number of rows ($N\ge 2$) in$Y$ direction and is infinite in $X$ direction. The spectrum of the linearwaves (Josephson plasmons) consists of $2N-1$ branches. Among these branchesthere is a $N$-fold completely flat degenerate one that coincides with theJosephson plasma frequency. The remaining $N-1$ branches have a standardJosephson plasmon dispersion law typical for 1D JJ arrays. Application of theuniform dc bias on the top of each vertical column of junctions lifts thedegeneracy and only one flat branch remains unchanged. The rest of thepreviously flat branches become weakly dispersive. The parameter range wherethe flatness of these branches is maximal has been discussed.

Flat and almost flat bands in the quasi-one-dimensional Josephson junction array