In this book, the theoretical researches refers to physico- and matehematical modelling of a separation machine with conical sieve vibrating suspended which is imparted a alternative circular motion with small amplitudes of horizontal oscillations. Also, in the book is made the theoretical study on the surface of conical sieve and determine the sieve amplitudes oscillation on a physical model simplified. Experimental facilities used in theoretical studies and experimental researches was conceived, designed and built to test them to propose that separation equipment for exploitation.