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Oscillation property (OP) is a fundamental qualitative property for free vibrations of single span one-dimensional continuums,such as bars,torque bars,Euler beams.To avoid qualitative errors in numerical methods,reasonable discretization of these continuums should maintain the property.In previous researches,the discrete OP is discussed more essentially by means of matrix factorization.Besides,the discussions are model-specific and lack of uniformity.In this paper,another approach is proposed to discuss OP through an equivalent statics qualitative property.In this alternative approach,OP of some commonly used discrete models of beams is proved uniformly with an assumption.It is found that the 2-nodes finite element beams via Heilinger-Reissener principle (HR-FE beams) as well as the 5-points finite difference (FD) beams possess this property unconditionally,while the 2 nodes finite element beams via potential energy principle (PE-FE beams) possess the property conditionally.