On the basis of a simple model of Czochralski crystal growth method, a theoretical analysis of crystal-meniscus system behaviour has been carried out. It has been shown that in a finite radius crucible, mutual influence of crystal radius and meniscus height leads to the possibility of their autooscillation. The dependence of autooscillation characteristics on crystal growth model parameters has been analysed. It has been shown that the amplitude of autooscillations decreases with the increase of crystal radius/crucible radius ratio. Numerical estimations for LEC GaAs crystal growth have been made. The problems of crystal radius control in this connection are discussed.