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The natural vibrations are inherent structural property for all structures, which respond with selective vibration in their most flexible direction. The determination of the inherent vibration properties is necessary for a reliable prediction of the dynamic response of the structure. The objective of this research is to create adequate mathematical models that enable a more realistic determination of the magnitude and shape of the structural vibrations in complex geotechnical construction systems that physically represent infinite half-space. An example is given for a composite vibration system consisting of a retaining wall and the surrounding soil half-space, usually composed of a basal semi-infinite soil environment and/or the semi-infinite soil environment behind the wall. This represents a complex flexible coupled system. The determination of the expected dynamic behavior of this system, which includes both the local stability of the wall and the global stability of the composite system as a whole, requires development of sophisticated numerical methods and models. As in any dynamic analysis, the first step is to define proper magnitudes and mode shapes for the system in question, which represents a complex task burdened with insufficiently clarified phenomena. The results of different models of retaining walls in elastic half-space, analyzed with the software packages SAP2000 and ADAD-IZIIS, indicate that the application of boundary elements of the type "spring elements" or "infinite elements" enables a precise simulation of the effects the infinite half-space exerts on the shape and the value of the dominant vibrations.
