Some equations of linear elasticity are developed, including those specific to certain actuator structures considered in formation theory. The invariance of the strain-energy under the transformation from rectangular to spherical coordinates is then established for use in two specific formation problems. The first problem, involving an elastic structure with a cylindrical equilibrium configuration, is formulated in two dimensions using polar coordinates. It is shown that L² controls suffice to obtain boundary displacements in H^1/2. The second problem has a spherical equilibrium configuration and utilizes the elastic equations in spherical coordinates. Results similar to those obtained in the two dimensional case are indicated for the three dimensional problem.