Abstract: With the aid of Routh's equation for non-holonomic constraints the motion equations of a nonlinear rotor-bearing system are derived by the modal synthesis method, considering all the algebraic and the differential linking conditions. Sub-harmonic resonance of the system are solved by an equivalent linearization method, which transforms the problem from solving differential equations into solving algebraic equations. This technique significantly simplified the analysis procedures and improves the computational efficiency. The effect of the differential linking condition on sub-harmonic resonance are studied quantitatively by analyzing the computational results fitting different kinds of the linking conditions. The results show that the differential linking conditions have a significant influence on sub-harmonic resonance. Thus, the differential linking conditions need to satisfy, which does not affect the computational efficiency even though the derivation effort and assembled matrix rank are increased.