Abstract In this paper an approximate earthquake analysis is presented for multistory building structures. The building is stiffened by an arbitrary combination of lateral load-resisting subsystems (shear walls, frames, trusses, coupled shear walls, cores). We consider stories with identical stiffnesses and masses, however the mass at the top floor may be different. The analysis is based on the continuum method. The spatial vibration problem of the replacement beam is solved approximately. Simple formulas are given to calculate the periods of vibration and internal forces of a building structure subjected to earthquakes. The utility and accuracy of the method is demonstrated by two numerical examples, in which the approximate solution is compared with finite element calculations.