Systems, methods, and articles of manufacture for physically-based sculpting of virtual elastic materials are provided. The physically-based sculpting in one embodiment simulates elastic responses to localized distributions of force produced by sculpting with a brush-like force (e.g., grab, twist, pinch, scale) using one or more regularized solutions to equations of linear elasticity applied to a virtual infinite elastic space, referred to herein as “regularized Kelvinlets.” In other cases, compound brushes, each based on a regularized Kelvinlet, may be used for arbitrarily fast decay; a linear combination of brushes based on regularized Kelvinlets may be used to impose pointwise constraints on displacements and gradients; locally affine forms of regularized Kelvinlets may be used for certain sculpting brushes; brush displacement constraints may be imposed by superimposing regularized Kelvinlets of different radial scales; and symmetrized deformations may be generated by copying and reflecting forces produced by regularized Kelvinlets.