A shoebox-shaped room with an absorbing ceiling, and otherwise rigid surfaces, is a common but hard case in room acoustics. Geometrical acoustics fails to predict the low-frequency effects and often also the high-frequency flutter echo effects in such rooms.Here, the ”surface impedance” method [Pavic & Du, 4278-4286, Internoise 2016] is used, employing the modal solution for a shoebox-shaped room. The absorbing ceiling can be represented by a set of secondary sources, and their vibration velocities are dictated by a matrix equation, where one has the choice to describe the absorber as a locally-reacting material or as an extended-reaction material. The final solution is a sum of the primary source and the secondary source contributions. The frequency-domain formulation is furthermore used to generate band-pass filtered impulse responses, which reveal the temporal decay shape. In this study, horizontal or vertical modes are excited by using sets of primary monopoles sources. Results demonstrate that a ceiling with an idealized frequency-independent, locally reacting absorber gives a strongly frequency-dependent reverberation time for horizontal modes. Results are compared with reference results calculated with the finite element method.