  In this work, we study the Cauchy problem of the Elastic Beam equation with
initial value in weighted Sobolev space $H^{1,1}(\mathbb{R})$ via the
$\bar{\partial}$-steepset descent method. Begin with the Lax pair of the
Elastic Beam equation, we successfully derive the basic Riemann-Hilbert
problem, which can be used to represent the solutions of the Elastic Beam
equation. Then, considering the solitonless region and using the
$\bar{\partial}$-steepset descent method, we analyse the long-time asymptotic
behaviors of the solutions for the Elastic Beam equation.
