An approximate method is presented to estimate the maximum lateral drift demands in multistory buildings with nonuniform lateral stiffness responding primarily in the fundamental mode when subjected to earthquake ground motions. The method is aimed at the estimation of the maximum roof displacement and of the maximum interstory drift ratio for a given response spectrum. A simplified model of the multistory building is used based on an equivalent continuum structure with nonuniform lateral stiffness distribution consisting of a combination of a flexural cantilever beam and a shear cantilever beam. The effect of the type and amount of reduction in lateral stiffness along the height of the building and of the ratio of overall flexural and shear deformations on the ratio of the spectral displacement to the roof displacement and on the ratio of the maximum interstory drift ratio to the roof drift ratio is investigated. It is shown that reductions in lateral stiffness along the height have a negligible effect on the ratio of spectral displacement to maximum roof displacement and only a small effect on the ratio of maximum interstory drift ratio to roof drift ratio. The use of the method is exemplified with a ten-story steel moment-resisting frame building with nonuniform lateral stiffness. Results computed with the simplified method are compared with those computed using linear and nonlinear time history analyses. It is shown that the method provides good approximations that are adequate for the preliminary design of new buildings or for a rapid evaluation of existing buildings.