This eBook is the second in a series of books on the critical earthquake response of elastic-plastic structures or rigid blocks under near-fault ground motions, and includes four original research papers which were published in the specialty section Earthquake Engineering in 'Frontiers in Built Environment'. Several extensions of the first book1 are included here. The first article is on the soil-structure interaction problem. The reduction of an original soil-structure interaction model into a single-degree-of-freedom (SDOF) model enables the application of the original theory for an SDOF model to such complicated soil-structure interaction model. The second article is concerned with the extension of the original theory for an SDOF model to a 2DOF model. Since the simple application of the original theory for an SDOF model to a multi-degree-of-freedom model is difficult due to out-of-phase phenomenon of multiple masses, a convex model theory is introduced and an upper bound of elastic-plastic response is derived. The third article is related to the stability problem of structures (collapse problems of structures) in which the P-delta effect is included. It is shown that the original theory for an SDOF model with elastic-perfectly plastic restoring-force characteristic can be applied to a model with negative second slope. The fourth article is an application of the energy balance approach to an overturning limit problem of rigid blocks. A closed-form expression of the overturning limit of rigid blocks is derived for the first time after the Housner's pioneering work in 1963. The approach presented in this book, together with the first book, is an epoch-making accomplishment to open the door for simpler and deeper understanding of structural reliability of built environments in the elastic-plastic and nonlinear range.