This paper investigates the intertubular van der Waals interactions that produce the initial cross sectional distortion of single-walled carbon nanotubes during a bundle formation. By combining the analysis of molecular dynamics with the continuum mechanics, the distributions of the van der Waals forces were determined. The dependence of the load parameters, deformation variables and the lattice constant on the nanotube radius, was also investigated. It was found that the van der Waals forces are attractive and vary circumferentially in a harmonic manner. For the considered zigzag nanotubes of radius 7-14 angstrom, the intensity of the van der Waals forces is radius-dependent and can be as large as 6-11 GPa in the channels of the bundle and 1-5 GPa at the closest points between the single-walled nanotubes.