The sway profile and sway quantities of a three dimensional structure must be known during the design process, in order to satisfy the criteria required in the design codes. Presently, the sway data of buildings is obtained by available computer programs. Even though sway data can readily be obtained by computer programs, during the preliminary design stage where cross-sectional dimensions are not yet finalized, repeated sway calculations become necessary, until code restrictions are satisfied. Therefore, the design engineer needs a method to calculate sway, which is realistic as well as quick and simple. Such a procedure may provide very practical solutions in the performance evaluation of existing structures. In this study, rather simple analytical relationships are developed to calculate sway of framed and shear wall-frame buildings, based on general differential equations of equilibrium. It is clear that such sway calculation methods will facilitate the efforts required in calculation of sway of building structures.