We address the optimal design of elastic structures by combining gradient-flow–based shape optimization with topological derivatives [7]. The design problem is posed as a constrained minimization in linear elasticity, where the objective quantifies structural performance (e.g., compliance or strain energy) under prescribed loads and boundary conditions, while constraints enforce a target volume (mass) and, when needed, additional regularity consistent with manufacturing requirements. A continuous gradient flow on the design space is introduced to generate a stable descent trajectory of the objective [6]. Constraints are enforced via projection or augmented- Lagrangian–type mechanisms. Shape sensitivities [8, 1] are complemented by topological derivatives [5, 2, 4, 3], which measure the first-order effect of creating an infinitesimal cavity or inclusion and therefore provide a principled criterion for nucleation, merging, and removal of material. We present an algorithmic framework coupling a time-discretized gradient flow with topology updates driven by the topological derivative. This coupling improves robustness, reduces dependence on initialization, and enables discrete connectivity changes that are difficult to capture by purely shape-based evolution. Numerical examples in two-dimensional linear elasticity illustrate the emergence of mechanically efficient layouts with clear load paths while satisfying volume constraints. The approach naturally extends to multiple load cases, perimeter control, and additional engineering constraints.