A normal‐mode model, including absorptive effects and elastic waves in the ocean floor, is presented for a source in the water column and a receiver in the water or the elastic medium. The appropriate boundary conditions between all liquid and solid layers are taken into account, and an absorptive semi‐infinite basement is assumed, which causes the radiating wave‐number spectrum to be discrete. The adiabatic approach has been adopted for the case where the acoustic properties or the boundaries vary slowly with range. Results of these calculations display the importance of even a slight range dependence, and of bottom elasticity in shallow‐center sound propagation.