It is known that a phenomenon referred to as wedging can occur in mechanical systems with friction. This phenomenon occurs in certain system positions, and an actual mechanical system can be started from a wedged position only at the cost of irreversible deformations. Although the results of the theoretical study of wedging are of great importance in the development and operation of process automation systems, the theory of this phenomenon is still in the making. In this work, the notion of a wedgeable system is introduced and its rigorous definition is given. Within the framework of the traditional formulation, this definition reflects the properties of wedging in actual mechanical systems in the most adequate manner. Based on this notion, a number of statements on wedging conditions in mechanical systems with two and three frictional contacts are proved. Simple, convenient in use rules are given for identifying the possibility of wedging in peg-in-hole systems with two and three frictional contacts.