Trapped modes are localized oscillations which have finite energy, and their existence in acoustic guides at wave numbers below the first antisymmetric cut-off has been well-documented. For wave numbers above the cut-off, the eigenvalue associated with the trapped mode is said to be embedded in continuous spectrum of the relevant operator. Here the authors investigate the existence of branches of embedded trapped modes in a vicinity of a rectangular block which is placed on the centreline of a two-dimensional acoustic waveguide. First, the trapped mode potential for the rectangular block is written out in terms of eigenfunction expansions in two separated regions, along the boundary of which an integral equation for the horizontal velocity is derived. Then, a simple approximation to the trapped mode potential leads to a transcendental equation for the wavenumber non-dimensionalized by the plate length. This equation is investigated in detail, and information about the branch stucture of the trapped modes is obtained.