In the first part of the talk inverse deformation analysis is revisited. The objective of inverse deformation analysis is to determine the undeformed configuration of an object such that it attains a known deformed configuration under the action of a known loading. A key component of this approach is the inversion of the deformation gradient. However, previous works have introduced inconsistencies by neglecting a crucial sign change. In this work, we present a corrected and rigorous derivation of the inverse deformation gradient that resolves this issue. Furthermore, we introduce an efficient implementation that significantly reduces the computational effort.Numerical examples demonstrate that the exact undeformed shape can be recovered in a single step, with practical implementation realized via AutoFreeFEM. In the second part of the talk we extend this inverse deformation analysis framework to optimal design problems. In such a setting the deformed shape is only partially fixed on a prescribed boundary, while other boundaries can be optimized to minimize material consumption under stress constraints. Again it is shown that also this shape optimization problem can be easily implemented via AutoFreeFEM.