The paper presents the connected evolutionary and gradient identification of the internal defects in an elastic body under dynamical load. The identification proceeds on the basis of the knowledge about boundary displacements in some sensor points. In the first step the evolutionary algorithm (EA) identifies the number, kind, position and size of internal defects. The fitness function is computed with the help of the pseudo-gaussian fuzzy inference systems (PGFISs). In the second step the gradient method of identification is used to obtain more precise results. The structure of the chromosome and the connection between the EA and the PGFIS is presented. The results of identification in an elastic rectangular under sinusoidal load with internal defects in the form of crack or circular voids are shown.