Composite laminates featuring curvilinear fibre paths show improved buckling resistance relative to straight-fibre laminates. In the present work, the prebuckling and buckling behaviour of variable-stiffness composite panels containing cutouts is investigated using a semi-analytical energy-based formulation. Panels with various in-plane and out-of-plane boundary conditions and cutout sizes and shapes are considered. The prebuckling stress field is obtained from the principle of stationary complementary energy, while the buckling problem is formulated using the total potential energy principle. Legendre polynomial expansions approximate the Airy stress function and displacements, with enriched trial functions capturing stress redistribution due to curvilinear fibres and cutouts. The internal energy integrals are evaluated numerically over both the full rectangular panel domain and the cutout region, with the internal energy contribution of the cutout subtracted from that of the full domain. Validation against reference solutions and finite element results shows good agreement, demonstrating the formulation’s reliability in predicting the stability of variable-stiffness composite panels with cutouts.