A superposition of coherent states, a ”cat-state”, can be treated as a quantum superposition of macroscopic states. In this thesis, I show how mechanical ”cat-states”, entangled to qubit states that describe electric degrees of freedom of the system, are generated in nanoelectromechanical (NEM) system. The examined NEM system consists of a movable superconducting quantum dot that harmonically oscillates between two bulk superconductors. The bulk superconductors are connected to a a controllable bias voltage. The induced charge on the quantum dot can be controlled via the gate voltage. By the special choice of parameters, the charge population (number of Cooper pairs) on the quantum dot can be described as a qubit system. As the quantum dot oscillates between the bulk superconductors, Cooper pairs tunnel from the bulk superconductors to the quantum dot and vice versa. This couples electrical and mechanical degrees of freedom of the quantum dot. Under the special protocol of controlling the bias voltage, the evolution of the system leads to the creation of mechanical ”cat-states”. In this thesis, firstly I derive the Hamiltonian of the system. After that the evolution of the system is calculated analytically using rotating wave approximation. In the main part, I present exact numerically calculated evolution of the system and I also take more realistic assumptions to consideration. Finally, the obtained states are characterized by the entanglement entropy and the Wigner function. The Wigner function of cat-states displays negative parts which is a signature of non-classical behaviour typical for the cat-states.