This paper presents a new algorithm to simulate the seismic response of N-story building frames incorporating friction energy dissipators; a device per floor is considered. The frames with the dissipators are described by 2D lumped masses models with two degrees of freedom per floor, namely the horizontal displacements of the main structure and of the dissipators. The proposed algorithm consists of a modification of the linear acceleration method; the main innovation consists of checking at each calculation instant the sliding or sticking condition at each floor, hence, the number of “active” degrees of freedom changes continuously, ranging in between N (there is sticking condition at every dissipator) and 2N (there is sliding condition at every dissipator). Some results given by this algorithm are compared to experimental results from ad-hoc testing and to numerical results obtained with the ADINA software package. In both cases, agreement is satisfactory while the proposed method is more computationally efficient.