The main goal of the paper is to show great potential of Artificial Neural Networks (ANNs) as a new tool in the identification analysis of various problems in mechanics of structures and materials. The basics of ANNs are briefly written focusing on the Back Propagation Neural Networks (BPNNs) and their features and possibilities in the analysis of inverse problems. Two groups of problems are analyzed: I) BPNNs are used in five problems as independent tools for the parametric identification and implicit modelling of physical relations, II) BPNNs are parts or procedures in three hybrid FEM/ANN systems or programs. Using measured eigenfrequencies the following problems are discussed: 1) identification of damage parameters of a steel beam, 2) attachment of an additional mass to increase the accuracy of prediction of damage parameters in a beam, 3) identification of location an additional mass attached to a steel plate. Implicit simulation of physical relations is discussed on two problems: 1) concrete fatigue durability of concrete as a function of concrete strength and characteristics of fatigue cycles (besides BPNN also the Fuzzy Weight NN was applied), 2) soil-structure interaction of displacement response spectra of a real building subjected to paraseismic excitations (besides BPNN the application of Kalman filtering is discussed for the NN learning). The following problems of Group II are investigated: 1) using BPNN in the hybrid Monte Carlo method for the reliability analysis of a steel girder, 2) application of BPNN to the calibration of control parameters in the updating of a FE program for dynamic analysis of a plane frame, 3) on-line methods for the NN constitutive model formulation basing on measurements of structural displacements.