Abstract The aim of this article is to demonstrate and discuss the possibilities of the application of classical Timoshenko beam theory to problems of three-layered elastic beams with symmetric composition. In particular, the equivalent single-layer first-order shear deformation theory (FSDT) with the variation of Timoshenko shear coefficient is applied. Three common types of beams are chosen for this study: (i) a beam composed of two stiff thick plies bonded by a thin soft layer, (ii) a soft-core sandwich beam and (iii) a beam of sandwich-like composition having a core stiffer than the face sheets. The possibilities of the application of FSDT to these basic types of beams and their modifications are studied on their transient responses to a pulse of impact character. Comparing the FSDT results with the results of the exact two-dimensional theory under the assumption of plane stress problem, the limits and the precision of FSDT are discussed. It is shown that FSDT can give very precise results in the case (iii), quite good results in the case (i) and questionable results for soft-core sandwiches.