When combining the Newton-Raphson method with the transfer matrix method to solve the steady-state balance position of a flexible rotor supported by hydrodynamic bearings, one commonly faces sensitivity issues with initial values that make the iterative process difficult to converge. This paper proposes a novel method using virtual spring-assisted constraints, which effectively and conveniently addresses this problem. A specific computational example is provided to demonstrate that the proposed method achieves good convergence without relying on preliminary estimates of initial values. This paper also highlights the need for the virtual spring to have high stiffness. The iterative process described by the novel method conforms to actual physical behavior and is easy to understand intuitively and implement programmatically.