The book outlines special approaches using singular and non-singular, multi-domain and meshless BEM formulations, hybrid- and reciprocity-based FEM for the solution of linear and non-linear problems of solid and fluid mechanics and for the acoustic fluid-structure interaction. Use of Trefftz functions and other regularization approaches to boundary integral equations (BIE), boundary contour and boundary node solution of BIE, sensitivity analysis, shape optimization, error analysis and adaptivity, stress and displacement derivatives in non-linear problems smoothing using Trefftz polynomials and other special numerical approaches are included. Applications to problems such as noise radiation from rolling bodies, acoustic radiation in closed and infinite domains, 3D dynamic piezoelectricity, Stefan problems and coupled problems are included.