The paper deals with the application of the Two-Stage Granular Strategy (TSGS) to the identification problems. Identification of selected parameters of the structures is performed. The identification problem is formulated as the minimization of some objective functionals which depend on measured and computed fields. It is assumed that identified constants and measurements have non-deterministic character. Three forms of the information granularity are considered: interval numbers, fuzzy numbers and random variables. The strategy combines the following techniques: Evolutionary Algorithms (EAs), Artificial Neural Networks (ANNs), local optimization methods (LOMs) and Finite Element Method (FEM). All techniques are appropriately modified to deal with non-deterministic data. The EA is used in the first stage to perform the global optimization. The LOM supported by ANN is used in the second stage. The FEM computations are performed to solve the boundary-value problem. Numerical examples presenting the efficiency of the TSGS in different applications are attached.