The purpose of this paper is to investigate a reinforced concrete multi-storey building with dissipative structural walls. These walls can improve the behaviour of a tall multi-storey building. The damage of a building with dissipative walls is compared with that of a building with solid walls. The comparative nonlinear dynamic analysis is performed by means of the SAP2000 software, using a layer model. In order to increase the seismic performance of a building with structural walls is to create slit zones with short connections into the walls. The short connections are introduced as a link element with multi-linear pivot hysteretic plasticity behaviour. The hysteretic rules and parameters of these short connections were proposed by the authors and used in this study. Using the proposed computational model for the slit wall, a seismic analysis of a multi-storey building with slit walls was done. From the results obtained, the advantages of the proposed model are observed. Unlike other studies on slit walls with short connections, which are focused mostly on the nonlinear dynamic behaviour of the short connections, in this paper the authors take into consideration the whole structural system, wall, connections and frames.