A linear approximation procedure has been applied to the derivation of shading coefficients for minor lobe control from symmetrical, but possibly irregularly shaped, transducer arrays, for which the relationship between the coefficients and output pressure is linear. Examples are included for the traditional problems of finding optimum coefficients for uniform and low minor lobe response from planar arrays, including one of a ’’honeycomb’’ array on a hexagonal grid, which could not be handled by analytical methods employed hitherto.Subject Classification: [43]85.40; [43]30.85; [43]20.55; [43]85.84.