The paper deals with the structural analysis of the mechanisms with elastic connections. This study is based on the up-to-date development of the technologies in the field of smart compound materials with controlled elastic deformation and the nanotechnologies. The aim of the study is to define the elastic connections in the context of the classical mechanism theory and to develop the relationships in order to compute the mobility of the mechanisms with elastic connections. In order to illustrate the theoretical development, the authors present several numerical examples. All methods are based on preserving of the kinetostatic conditions in a movement cycle. The authors present the classification of elastic connections in correlation with the classical ones.