A continuum formulation of the van der Waals interactions between carbon onion layers in form of pressure/radius relations is obtained. The relations are derived analytically considering the doubly-curved geometry of carbon onion layers. For finite layer radii it is shown that the van der Waals induced pressures on opposing faces of two adjacent onion layers are not equal and depend on both layer radii. Equilibrium configurations of different double-layer onion models are calculated using the theorem of stationarity of the total potential energy. The results are compared with those of simplified models which do not consider any curvature effects. It is shown that curvature effects have no significant influence on the equilibrium interlayer distances, but they significantly change the results for the radial displacements and, consequently, for the membrane forces in the layers. Comparison with Monte Carlo simulations of C60 in C180 and C60 in C240 shows that the derived van der Waals model represents the radial displacements and equilibrium interlayer distances better than the simplified models. Thus, whenever a good representation of the membrane forces is important, e.g., in stability analysis, the new approach should be used.