Back analysis problems, also known as inverse problems or characterization problems, can be formulated as parameter estimation problems, by which means two basic types of problems can be solved: i) Determination of external loads from the structural properties and from observed response, sometimes called inverse problems of the first kind; ii) Determination of structural properties parameters as a function of the external loads and observed responses, sometimes called inverse problems of the second kind. The structural properties are defined by the geometry of the structure and by the properties and zoning of the different constituent materials. The observed effects (displacements, unit strains, stresses, etc.) represent the structural response. The former type of problems corresponds to the determination of the actions on basis of structural properties and of observed effects, whereas the latter refer to the deter­ mination of the characteristics parameters of the structural properties on basis of actions and corresponding observed effects. Back analysis problems can be solved in two ways, which Cividini calls direct approach and inverse approach (Cividini et al., 1981). The direct approach uses the same numerical solutions as the direct analysis, determining the val­ ues of the parameters in accordance to some identi­fication criteria, corresponding, for instance, to the least square, Markov or maximum likelihood meth­ ods (Eykhoff, 1974). The inverse approach requires a reformulation of the problem equations in such a form that the observed effects correspond to known quantities whereas the parameters to be identified appear as unknown. Direct approach methodologies allow the identi­fication of model parameters related with actions or with structural properties (in particular, with mater­ ial properties), which includes the combined use of a numerical model and of an adequate minimiza­tion method. This approach is less sensitive to the quality of the observed values and to the degree of approximation of the numerical model. An impor­tant feature of these methodologies is the separate use of the numerical model and of the minimiza­tion method, which allow the use of complex mod­ els developed in commercial programs (without access to its code). Inverse approach methodologies allow, in princi­ple, faster convergence taxes than direct approach methodologies. Nevertheless, these methodologies are more sensitive to the quality and to the quanti­y of the observed effects and require numerical models that can reproduce approximately the observed response. Usually, the resolution of specif­ ie problems requires the development of specific codes since it is difficult or even impossible to adapt commercial programs to this purpose. In the next paragraphs three different back analysis approaches will be presented.