This study presents a general higher-order 1D theory and its nonlinear finite element model for tubular structures undergoing large deformation, considering a general anisotropic hyperelastic material with two families of fibers. To map the geometry of the structure, we considered a general hybrid-frame based curved cylindrical coordinate system (see [1]), which is capable of mapping both a well-defined and an approximated reference curve (back-bone curve) of tubular structures. To approximate the general displacement field of the cross-section of the tube, we considered Fourier bases in the θ-direction and a power series in the r-direction. Based on this approximation, the kinematics are derived in a curved cylindrical coordinate system using an orthonormal moving frame (see [1]), which significantly reduces the algebraic complexity compared with the classically considered natural covariant basis. Further, by applying the principle of virtual displacement in the reference configuration ([2]), we derived the governing equations as a system of nonlinear ordinary differential equations in the arc-length coordinates. Subsequently, we develop a 1D nonlinear finite element model to solve the governing ODE for given boundary conditions. We further specialized the general anisotropic hyperelastic material model to the Holzapfel–Gasser–Ogden model for a two-fiber family for an application in arterial mechanics. The formulation is applicable to both thin- and thick-walled tubular geometries such as arteries, veins, gastrointestinal segments, fibre-reinforced soft conduits, and soft robotic actuators. We present various numerical examples demonstrating comparisons with shell-theory predictions, as well as the computational efficiency and cost-effectiveness of the proposed framework.