This study proposes a modeling method based on absolute nodal coordinate formulation (ANCF) with internal constraint equations for highly flexible and deployable aerospace structures such as truss antennas, manipulators, and deployable/folding wing aircraft. ANCF is a nonlinear finite element method used in the deployment simulation owing to its ability to express large rigid body motion and elastic deformation, constant mass matrix, zero imaginary force, and simple description of constraint equations. However, the application of a three-dimensional (3D) ANCF beam element to complicated cross-sectional structures (e.g., wing) has been difficult, because the elastic force is derived from the volume integral of the elastic energy using Green–Lagrange strain and Lame’s constants, namely continuum mechanics approach. To overcome this difficulty, a new elastic force formulation is proposed based on an element coordinate approach, internal constraint equations, and a Frenet–Serret equation. We name the proposed formulation as absolute nodal coordinate formulation with internal constraint equation (ANCF-ICE). The new formulation provides a 3D ANCF Euler– Bernoulli beam element that can express torsion without the use of rotational angles. The ANCF-ICE beam element successfully simulates the wing deployment of a flexible aircraft flying in 3D space.