Asymptotic formulae are derived for the fields of displacements, strains and stresses near a peak-shaped protrusion in the surface of an anisotropic elastic body (a "claw"-type singularity). The singular solutions constructed are interpreted as forces and torques concentrated at the tip of the peak, while the orders of growth of the displacement depend on the direction of the action of the force (longitudinal or transverse) and of the axis of the torque (twisting or bending) but not on the elastic properties of the material. The asymptotic analysis makes essential use of the observed analogy with one-dimensional models of thin rods of variable cross-section.