The characteristics of civil structures inevitably suffer a certain level of damage during its lifetime and cheap, non-destructive and reliable methods to assess their correct performance are of high importance. Structural System Identification (SSI) using measured response is the way to fine why performance is not correct and identify where the problems can be found. Different methods of SSI exist, both using static and vibration experimental data. However, using these methods is not always possible to decide if available measurements are sufficient to uniquely obtain the unknown. A (SSI) method that uses constrained observability method (COM) has already been developed based on the information provided by the monitoring of static non-destructive tests - using deflections and rotations under a known loading case. The method assures that all observable variables can be obtained with the available measured data. In the present paper, the problem of determining the actual characteristics of the members of a structure such as axial stiffness, flexural stiffness and mass using vibration data is analyzed. Subsets of natural frequencies and/or modal shapes are used. To give a better understanding of the proposed method and to demonstrate its potential applicability, several examples of growing complexity are analyzed, and the results show how constrained observability techniques might be efficiently used for the dynamic identification of structural systems using dynamic data. These lead to significant conclusions regarding the functioning of an SSI method based on dynamic behavior.