In this paper, we propose a set of free-form shape deformation techniques. The basic approach can be described as follows. Given a surface represented by a mesh and a control point, for every mesh vertex let us consider the difference between the control point and the vertex. The vertex is shifted by a displacement equal to the difference times a scale factor where the scale factor is given by a function depending nonlinearly on the difference. The function is bump-shaped and depends on a number of parameters. Varying the parameters leads to a rich palette of shape deformations. The proposed approach includes also shape deformations with multiple (real, auxiliary, and virtual) control points and constrained, directional, and anisotropic deformations. It allows a user to edit a given shape interactively and intuitively. No mesh connectivity information is used and, therefore, the proposed techniques can be applied directly to a shape given as a cloud of points.