  We investigate -- through simulations and analytical calculations -- the
consequences of uniaxial lateral compression applied to the upper layer of
few-layer graphene. The simulations of compressed graphene show that strains
larger than 2.8 \% induce soliton-like deformations that further develop into
large, mobile folds. Such folds were indeed experimentally observed in graphene
and other solid lubricants two-dimensional materials. Interestingly, in the
soliton-fold regime the shear stress decreases with the strain s, initially as
$s^{-2/3}$ and rapidly going to zero. Such instability is consistent with the
recently observed negative dynamic compressibility of two-dimensional
materials. We also predict that the curvatures of the soliton-folds are given
by $r_c = \delta\sqrt{\beta/2\alpha},$ where $1\le \delta \le2,$ and $\beta$
and $\alpha$ are respectively related to the layer bending modulus and to the
exfoliation energy of the material. This finding might allow experimental
estimates of the $\beta/\alpha$ ratio of two-dimensional materials from fold
morphology.
