In the seismic analysis of nuclear power plants, the time history method is used as one of the techniques of dynamic analysis. Many problems such as an idealization of dynamic model, an assessment of damping coefficients and the soil-structure interaction are involved in this method. Since the time history method is usually carried out in the elastic range, the ultimate behavior of structure to some extent still remains unknown after those problems were solved. Thus, a computer program was developed to investigate the elasto-plastic behavior of structures. The purpose of this paper is to present the outline of this program and to discuss the problems of nonlinear response of structures. There are two theoretical methods in the time history approach, that is, the mode superposition method and the direct integration method. Since the mode superposition method is only valid in an elastic analysis, the direct integration method was adopted here. As the sample model, an actual reactor containment (reactor building) of a PWR plant was adopted. This building consists of three components: a concrete internal structure, a steel containment vessel and a concrete outer shield wall. These components rest on a rigid foundation mat. Therefore they were modeled with a lumped mass model, respectively, and coupled on the foundation. The following assumptions and procedures were employed to establish the properties of the dynamic model and to carry out the response analysis: 1. (1) Rocking and swaying springs of soil can be obtained from an elastic half-space solution. The nonlinear rocking spring can be considered when a foundation mat detaches from the soil. On its hysteretic characteristic, both bilinear and spring types are studied and employed in the response analysis. 2. (2) Springs connecting each mass are dealt with shear beams so that both bending and shear deflections can be included. The hysteretic characteristics of each spring of the containment vessel and the outer shield wall are determined to be either bilinear or trilinear according to its intensity and the springs of the internal structure are linear. 3. (3) Two kinds of hysteretic loops are studied and used in the response analysis. 4. (4) Generally a particular damping coefficient is given for each mode in mode superposition. However, a damping matrix must be made directly in a nonlinear response. Therefore the damping matrix of the model was made by combinining the damping matrices [ C] of each component obtained by Cauchy's method and a damping value of the rocking and swaying by the half-space solution. 5. (5) Two earthquake waves of El Centro 40 NS and Golden Gate E-W are used with modifying 300, 450 and 600 gal. On the basis of above conditions, the nonlinear response of the structure was obtained and the difference between elastic and elasto-plastic analysis is presented.