The paper presents a novel numerical method for structural optimization that combines the classical shape derivative with the level-set method for front propagation. This method is implemented in two and three space dimensions for models of linear or nonlinear elasticity, considering various objective functions with weight and perimeter constraints. The shape derivative is computed using an adjoint method, and the cost of the numerical algorithm is moderate as the shape is captured on a fixed Eulerian mesh. The method can handle topology changes but is sensitive to the initial guess. The paper discusses different objective functions, including compliance, least square deviation from a target, and design-dependent loads. It also addresses the extension of the method to nonlinear elasticity models and the handling of multiple loads. The effectiveness of the method is demonstrated through numerical examples, including a cantilever problem, a bridge problem, and a gripping mechanism test case. The results show that the method converges smoothly to optimal shapes, which are mesh-independent and stable under different initial conditions.The paper presents a novel numerical method for structural optimization that combines the classical shape derivative with the level-set method for front propagation. This method is implemented in two and three space dimensions for models of linear or nonlinear elasticity, considering various objective functions with weight and perimeter constraints. The shape derivative is computed using an adjoint method, and the cost of the numerical algorithm is moderate as the shape is captured on a fixed Eulerian mesh. The method can handle topology changes but is sensitive to the initial guess. The paper discusses different objective functions, including compliance, least square deviation from a target, and design-dependent loads. It also addresses the extension of the method to nonlinear elasticity models and the handling of multiple loads. The effectiveness of the method is demonstrated through numerical examples, including a cantilever problem, a bridge problem, and a gripping mechanism test case. The results show that the method converges smoothly to optimal shapes, which are mesh-independent and stable under different initial conditions.