The interaction between one-dimensional (1D) beams and three-dimensional (3D) solid continua, particularly for beams embedded within a continuum, is a significant challenge in computational mechanics. The primary difficulty stems from the fundamental geometric mismatch between the 1D line representation and the 3D volumetric domain, which complicates interface definition and the consistent transfer of mechanical quantities. To resolve these issues, the Arbitrary Lagrangian-Eulerian (ALE) method provides an effective framework by controlling nodal movement to align the mesh with the evolving contact geometry [1]. This study extends the ALE formulation for elastic rods [2] to address these geometric challenges. Derived from the ALE framework for hyperelasticity [3], this method enables stress analysis with fixed spatial nodes by treating initial material coordinates as unknowns. While straightforward for stationary interfaces, applying this to sliding contact on deforming solids is a substantial task, as the contact location on the beam varies in accordance with the deformation of the continuum. To date, the potential of ALE-based approaches to handle such mixed-dimensional interfaces with deformation-dependent contact regions has not been sufficiently explored. This paper proposes a numerical procedure treating frictionless sliding as a boundary-following mesh motion problem. By strategically configuring degrees of freedom within the ALE framework, we circumvent the numerical pathologies of traditional methods, such as penalty sensitivity and saddle-point instability. Instead of enforcing standard constraint conditions, the frictionless sliding requirement is reformulated as a kinematic boundary condition prescribing the spatial motion of the ALE mesh. This allows beam nodes to glide tangentially along the solid surface, providing a robust solution to the geometric mismatch. The performance of the method is validated through several benchmarks involving large deformations. REFERENCES [1] S.Gosh, Arbitrary Lagrangian-Eulerian Finite Element Analysis of Large Deformation in Contact Bodies, International Journal for Numerical Methods in Engineering, 33, 1891-1925, 1992. [2] T. Yamada, Large deformation analysis of elastic rod by an arbitrary Lagrangian Eulerian finite element method, Trans JSCES, No.20050003, 2005(in Japanese). [3] T. Yamada and F. Kikuchi, An arbitrary Lagrangian Eulerian finite element method for incompressible hyperelasticity, Computer Met