In this paper the mutual coupling problem for finite waveguide array with impedance flange radiating into stratified media has been solved using variation principle. The problem has been reduced to set of integral equation for auxiliary finite functions. Auxiliary functions presented as an electrical and magnetic fields tangential parts linear combination on waveguide apertures. Stationary functional for this set of equation has been found. In single-mode approach this problem has been reduced to set of linear algebraic equations. Equations for reflecting coefficients and mutual coupling coefficients have been found.