The dynamic analysis of string-shaped flexible elements using Cosserat theory, faces significant challenges owning to their chaotic behavior. To address this, this study proposes a method for the static equilibrium analysis of cantilevered string-shaped flexible elements. First, the properties of the differential equations derived from Cosserat theory are examined using the phase space analysis. This allows the pattern of the curvature distribution at the minimum or maximum value of the equilibrium solutions to be identified. Based on these properties, we propose a method for identifying curvature distribution patterns for each equilibrium solution when multiple solutions exist, thereby estimating the arc shape configurations of the flexible elements. Additionally, we demonstrate that this estimation facilitates obtaining a desired static equilibrium shape using the bisection method. Finally, we demonstrate that the proposed method becomes increasingly effective for longer, slenderer, and more pliable flexible elements, thereby confirming its practicality in analyzing string-shaped flexible elements.