This paper is concerned with seismic analysis and design of structures with added viscoelastic (VE) dampers. Based on the experimental and analytical results obtained earlier, a seismic design procedure for structures with added VE dampers is proposed with an example illustrating the proposed design procedure. Comparisons on the seismic performance between the ~iscoelastically damped structure and a conventionally designed special moment resisting frame are carried out. It is shown that the proposed design procedure provides an alternative safe and economic solution for earthquake resistant structures under current seismic design regulations. In addition, it is shown that with a sufficiently large design damping ratio, such as 15 % in this study, structures with added VE dampers may remain elastic or experience only minor yielding under most current design earthquakes.