<p>In this paper, a novel isogeometric finite element formulation is developed to investigate buckling responses of curved Euler–Bernoulli nanobeams. The governing equations and standard boundary conditions are derived through the minimum total potential energy principle. The equivalent differential forms of the strain- and stress-driven two-phase local/nonlocal integral models, along with the corresponding constitutive boundary conditions, are considered in a unified form to account for the size effect phenomenon. The axial force and bending moment are explicitly obtained, and the weak form of the governing equation is derived accordingly. The isogeometric analysis (IGA)-based finite element method (FEM) is developed to obtain the novel isogeometric finite element formulation for the buckling behaviors of curved nanobeams under different boundary conditions, with the displacement field modeled by Non-uniform rational B-splines (NURBS) instead of traditional Lagrangian and Hermite cubic interpolation functions. The constitutive boundary conditions enable the flexible accommodation of higher-order variables. This two-phase isogeometric finite element model fulfills high-order boundary conditions, features straightforward shape functions, and exhibits favorable convergence behavior. The buckling analysis results are compared with other available results in the literature to demonstrate the efficiency and accuracy of the present IGA framework. Convergence and parameter sensitivity analyses conducted under various boundary conditions demonstrate the robustness of the proposed method. The numerical results show that the strain- and stress-driven two-phase local/nonlocal models of curved nanobeams exhibit consistent softening and stiffening effects on buckling responses, respectively. Additionally, the effects of the opening angle and length-to-height ratio of the curved nanobeam are investigated.</p>