The propagation of waves at tidal frequencies is studied analytically for simple configurations involving a wall, a channel, semi-enclosed basins, or a continental slope with adjacent shelf sea. The equations of motions are presented, and are simplified using the linear and hydrostatic approximations. The fundamental wave types (Poincaré and Kelvin waves) are derived. The appearance of amphidromic points is explained. A detailed analysis is provided of the solution of the Taylor problem in the case of perfect reflection. The parameter space is explored for modified Kelvin waves in the presence of a shelf sea. As a special case, the double Kelvin wave is obtained.